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Trigonometry Area and angles of iso triangle given find sides

karush

Well-known member
Jan 31, 2012
3,055
Given an Isosceles triangle with the area of 100 with internal angles of
$$40^o, 70^o,70^o$$
$A=\frac{1}{2}bh$
so
$100=\frac{1}{2}\left(z\sin\left({70^O}\right)\right)\left(2z\cos\left({70^o}\right)\right)$
$z$ is length of one the equal sides

At least started here
 
Last edited:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Consider the following diagram:

karush4.png

Now, using the Law of Sines, we may state:

\(\displaystyle A=B\frac{\sin(a)}{\sin(b)}\)

If we denote the area of the triangle with $A_T$, then we may also state:

\(\displaystyle A_T=\frac{1}{2}B^2\sin(a)\)

Now, just solve for $B$, and then you will know $A$ as well. Then you will have formulas that you can plug into the given data. :)
 

stud17

New member
Mar 3, 2016
1
Given an Isosceles triangle with the area of 100 with internal angles of
$$40^o, 70^o,70^o$$
$A=\frac{1}{2}bh$
so
$100=\frac{1}{2}\left(z\sin\left({70^O}\right)\right)\left(2z\cos\left({70^o}\right)\right)$
$z$ is length of one the equal sides

At least started here
I think what you have done is correct just remember that $\sin(2x) = 2\cos(x)\sin(x)$ to simplify.

Hello, Admin. How do I post a thread? No bottom to click. I can only reply. (Worried)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
...Hello, Admin. How do I post a thread? No bottom to click. I can only reply. (Worried)
If you browse to a forum, you will see, above and below the thread listing, large buttons labeled "+ Post New Thread" that will allow you to begin a new thread in that forum. :)