What is Right triangle: Definition and 88 Discussions

A right triangle (American English) or right-angled triangle (British), or more formally an orthogonal triangle (Greek: ὀρθόςγωνία, lit. 'upright angle'), is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of the right angled is the basis for trigonometry.
The side opposite the right angle is called the hypotenuse (side c in the figure). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus). Side a may be identified as the side adjacent to angle B and opposed to (or opposite) angle A, while side b is the side adjacent to angle A and opposed to angle B.
If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple.

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  1. X

    Right Triangle Maximization Problem

    This is a fairly standard maximization problem in calculus, but I was wondering if anybody could help me come up with a nice geometric solution. It seems like it should be possible to make an argument based on symmetry, but I haven't quite been able to work it out yet. Note, I have already...
  2. M

    Volume of cross sections using isosceles right triangle

    Homework Statement The area is bounded by the equation y=x^2, x-axis and the line x=3 and is perpendicular to the x axis Homework Equations A=1/2bh Height=Base The Attempt at a Solution A=1/2B^2 V=1/2B^2 from 0 to 3 V=1/2 B^3/3 from 0 to 3 V=B^3/6 from 0 to 3 V=27/6 please...
  3. G

    Solving Right Triangle question

    Homework Statement I am having trouble with right triangles. I understand how to use the formulas, however I don't know which angle is appropriate when using the formulas. For example, in this picture: http://imgur.com/C2lxg . There was a problem in my book that had a triangle like this. The...
  4. J

    Drawing a right triangle to simpliy the given expressions

    1. Homework Statement Sin(sec^-1(sqrt(x^2+16)/4)) 2. Homework Equations 3. The Attempt at a Solution I did the math and ended up getting x^2-1 as the opposite, but the answers on the back of the book say other wise.
  5. J

    Drawing a right triangle to simply the given expressions

    Homework Statement Cos(Tan^-1(x)) Homework Equations The Attempt at a Solution Dont know how drawing a right triangle would do anything, don't know what to plug in.
  6. J

    Relative Error of Right Triangle Area

    Homework Statement Anyone mind checking my answer for me? The area of a right triangle with hypotenuse H is A=1/4H^2sin(2x) x is one of the acute angles. Use differentials to estimate the relative errors of the area if H = 4cm exactly and x is measured to be 30degrees with an error of...
  7. D

    Radius of a circle that intersects two points on a right triangle.

    Homework Statement I'm trying to figure out the radius of a circle that intersects two points on a right triangle. One side of the triangle is tangent to the circle and the other intersects it. I have attached an image that helps further explain what I'm talking about. Knowing what I have...
  8. D

    Radius of a circle that intersects two points on a right triangle.

    I'm trying to figure out the radius of a circle that intersects two points on a right triangle. One side of the triangle is tangent to the circle and the other intersects it. I have attached an image that helps further explain what I'm talking about. Knowing what I have listed in the image is...
  9. L

    Trig right triangle solving question How do you know if you should pick tan40 degrees

    Trig right triangle solving question How do you know if you should pick tan, cot, etc for the last part? if b = 2 , A =40 , find a,c, and B I found all of them except for c , how do you get c There's a part almost at the end that goes like tan40 degrees = a/2 and Cos 40 degrees = 2/c Why do you...
  10. B

    Find max area of rectangle inside a right triangle.

    Homework Statement Find the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of lengths 5cm and 12cm. the two sides of the rectangle lie along the legs. Homework Equations N/a The Attempt at a Solution
  11. C

    Right triangle with four jointed links

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  12. D

    The force on one face of a right triangle is ?

    Homework Statement Problem: Find the force on one face of a right triangle of sides 4 meters and altitude of 3 meters. The altitude is submerged vertically with the 4 meter side in the surface. The selections by the way are a. 58.86 kNewton b. 53.22 kNewton c. 62.64 kNewton d...
  13. A

    Center of mass of right triangle, without calculus

    Homework Statement How can I find the center of mass of a right triangle, of height h, length a, and mass m, without using calculus? Homework Equations The Attempt at a Solution I just need a hint on how to start please
  14. F

    Finding the displacement of a non right triangle?

    Homework Statement A small map shows Atlanta to be 730 miles in a direction of 5 degrees north of east from Dallas. The same map shows that Chicago is 560 miles in a direction of 21 degrees west of north from Atlanta. Assume a flat Eath and use this information to find the displacement from...
  15. I

    Center of mass: mass's on a right triangle system

    A system consists of three particles located at the corners of a right triangle as shown below. Mass 1 is 7.0 kg, mass 2 is 6.4 kg, and mass 3 is 9.9 kg. If the distances a equals 15.8 m and b equals 2.0 m, then what is the center of mass (in m) in the vertical direction? Y center of...
  16. V

    Finding center of mass of a right triangle

    Homework Statement Find the center of mass for the following triange: http://www.ehow.com/how_5132033_calculate-hypotenuse.html above is a picture of a triangle, it is a right triangle the side labeled a in the picture is a length of 1 and side b is length of 2, the total weight of...
  17. F

    Moment of Inertia of a Right Triangle

    Homework Statement A metal sign for a car dealership is a thin, uniform right triangle with base length b and height h. The sign has mass m. What is the moment of inertia of the sign for rotation about the side of length h? Homework Equations I = \intr^{2}dm The Attempt...
  18. V

    Rate of change of a right triangle

    Imagine a boat on the water being putted towards the shore by a winch mounted a height h above the water. The winch reels in cable (shortening the hypotenuse) at constant rate u in m/s . When the boat is a distance d from the shore, find its speed and acceleration. This is an example of motion...
  19. Z

    Right triangle problem,please check

    Right triangle problem,please check! Homework Statement In the figure,TN=NK, ST=12 and SN=\sqrt{69}.Find the length of TK. [PLAIN]http://img695.imageshack.us/img695/633/50042657.png Homework Equations Pythagorean Theorem The Attempt at a Solution Segment SN is the median of the...
  20. Q

    Right triangle, describe dx as dθ

    1. Homework Statement This is part of a find the electric field problem. I've narrowed down the part I find confusing. Consider a right triangle, with legs of length x and R. Angle θ is opposite x. Leg x is a segment of a ray starting where lines x and R intersect. There is a differential...
  21. 1

    Right Triangle Question for physics problem

    Homework Statement given only the time in the air and the range horizontally of one projectile. How can i find the angle and velocity of the projectile? Homework Equations trig functions? The Attempt at a Solution not sure how...hints?
  22. L

    Geometry (Proof right triangle angle sum is 180)

    Hi guys not sure were this goes sorry... It's been a while sense I have taken geometry so my skills are a little rusty... It tunrs out that I need to prove that the angles in a right tranlge add up to 180 I have looked on the internet and people just tell me oh this angle and that angle...
  23. D

    How To Find Sides Of Right Triangle With Known Angles And Area?

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  24. B

    Show that the triangle is a right triangle

    If angles A, B, and C are the angles of a triangle such that sin(A+B)=1/sin(C) and cos(A+B)=cos(C), then show that the triangle is a right triangle.
  25. H

    Calculate the moment of inertia of a right triangle

    Homework Statement A right triangle has height 'h' and width 'b.' The right triangle has a constant area density. Calculate the moment of inertia of the triangle rotated around an axis that runs along side 'h.'Homework Equations I = integral(r^2*dm) where 'r' is distance from the axis The...
  26. B

    Solving for x in Large Right Triangle

    A large right triangle has a hypotonuse of 2000x+1125. The other sides are 2000x-1125 and x. solve for x. I have tried this with pythagoreon theorem and solving a quadratic and what not but can't get it to work out. maybe i am just making a simple mistake but i can't get it to work out.
  27. S

    Charges placed in right triangle pls HELP

    Homework Statement Charges q1, q2, q3 are placed in a right triangle. Charges are given, distance between charges is given. Find the electrical field strength at point "A" which is in the middle of the hypotenuse. Which equations and how would I figure that out knowing that I have to give...
  28. D

    Vector Cross Product (with Right Triangle)

    Homework Statement For the vectors in the figure below, with a = 8, b = 7, c = sqrt(113), give the magnitude and direction of the following cross products. (See attachment for figure/right triangle). (a) a x b (b) a x c (c) b x c Homework Equations \vec{A} \cdot...
  29. L

    Right Triangles within a right triangle. (Trig)

    "To Estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 32 degrees. One thousand feet closer to the mountain along the plain, it is found that the angle of eleveation is 35 degrees. Estimate the height of the mountain."...
  30. L

    Using Trigonometry to Find Distance from a Flagpole on a Hill

    1. A woman standing on a hill sees a flagpole that she knows is 60 ft tall. The angle of depression to the bottom of the pole is 14 degrees, and the angle of elevation to the top of the pole is 18 degrees. Find her distance x from the pole. 2. I draw a diagram of the problem with a person on...
  31. D

    NEED HELP Finding the length of an angle on a right triangle

    Homework Statement ---- l../ l./ l/ ^This is a right triangle (not drawn to scale). The left side is 18,944, then top side is 30,556, and the hypotenuse is 35,952. The right angel is between the left side and the top side. Now, how do I find the measurement of the angle between the hypotenuse...
  32. A

    Finding Area of a Right Triangle & Proving arctanx Limit

    Question1:In a right triangle,the sum of the lengths of the hypotenuse and a leg is 1.Find the largest possible area of such triangle. Question2:Prove that arctanx=pi/2-1/x+o(1/x)(x tends to +inf) Question3:evaluate lim(2arctanx/pi)^2 (x tends to +inf)
  33. M

    Moment of inertia of a right triangle

    in my homework the question wants from me to find the moment of inertia of right triangle with the y-axis as shown in the attatchment note: the mass of the plate is 1 kg i found the y coordinate of the center of mass of the plate it is 5/3 and i supposed it is the r so the inertia...
  34. F

    Distance calculation (right triangle)

    Homework Statement Starting from city A, a car drives 250 miles east to city B, then 300 miles north to city C, and then 700 miles west to city D. What is the distance between city A and city D? (Points: 1) 300 mi 400 mi 500 mi 600 mi Homework Equations A^2...
  35. U

    Rate of Change of x in a Right Triangle

    In a right triangle with sides x,y,z, the theta between leg z and leg y is increasing at a constant rate of 3 rad/min. What is the rate at which x is increasing in units per minute when x equals 3 units and z is 5 units. so the triangle is basically a 3,4,5 triangle. The theta is between the...
  36. A

    Prove this is a right triangle?

    How can I prove that a right triangle whose sides are n^2+1 , n^2-1, and 2n is indeed a right triangle? The hint is to use the pythagorean theorem which is a^2 + b^2 = C^2 . I don't know what to do? i tried squaring the 3 terms but I can't get the first 2 to equal the last term (term c which...
  37. T

    Center of mass of a right triangle

    Hey guys. this is my first time posting. can anyone tell me how to calculate the Y component of center of mass of a right triangle?? Major help would be appreciated :-D please email me at fakedoublebassdrummer@yahoo.com
  38. T

    Center of Mass of a Right Triangle

    Hey guys. this is my first time posting. can anyone tell me how to calculate the Y component of center of mass of a right triangle?? Major help would be appreciated :-D please email me at [email address deleted]
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