Right triangle problem,please check

In summary, the problem asks to find the length of TK in a right triangle where TN=NK, ST=12, and SN=\sqrt{69}. The Pythagorean Theorem is used to solve the problem by setting up two equations for two unknowns in the two right angled triangles on the picture. After following this method, the correct answer was obtained.
  • #1
zafer
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0
Right triangle problem,please check!

Homework Statement


In the figure,TN=NK, ST=12 and SN=[tex]\sqrt{69}[/tex].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 right triangle.Here its not given the other leg how can we find a or b ?
 
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  • #2


There are two right angled triangles on the picture. They have a common side. Although you do not know the length of it, I would suggest you mark it with some letter. Then, write out Pythagora's Theorem for both of them. You will have two equations for two unknowns.
 
  • #3


Yes,you are right, thanks a lot.I got the correct answer
 

Related to Right triangle problem,please check

1. What is a right triangle?

A right triangle is a type of triangle that has one angle measuring exactly 90 degrees, also known as a right angle. The other two angles are acute, meaning they are less than 90 degrees.

2. How do you find the missing side lengths of a right triangle?

To find the missing side lengths of a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as a^2 + b^2 = c^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

3. What is the difference between the legs and the hypotenuse of a right triangle?

The legs of a right triangle are the two shorter sides that form the right angle, while the hypotenuse is the longest side that is opposite the right angle. The legs are always perpendicular to each other, while the hypotenuse is the side that connects the two legs.

4. Can a right triangle have two equal sides?

Yes, a right triangle can have two equal sides, which would make it an isosceles right triangle. This means that the two legs are equal in length and the hypotenuse is longer than the two legs.

5. What is the special relationship between the sides of a 45-45-90 degree right triangle?

In a 45-45-90 degree right triangle, the two legs are equal in length and the hypotenuse is equal to the length of one of the legs multiplied by the square root of 2 (or about 1.414). This is a special relationship that can be used to find missing side lengths in this type of right triangle.

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