1. ## trig functions

I am working on a project, and I was wondering if you could find a length of a side of a right triangle by using the trig functions such as

sin A= opposite/hypotenuse, cos A=adjacent/hypotenuse, and

(I know you can use pythagoreans theorem, but I need to find another way to find the missing side)

If my example is
Town x is 9 miles from town y, and 12 miles from town z. A road connects towns y and z directly. Find the length of this road. 9^2 + 12^2 = c^2

how can i find the length of c using trig. functions? (I know c=15 by using pythagorean theorem)

Thanks

2. Originally Posted by mandy123
I am working on a project, and I was wondering if you could find a length of a side of a right triangle by using the trig functions such as

sin A= opposite/hypotenuse, cos A=adjacent/hypotenuse, and

(I know you can use pythagoreans theorem, but I need to find another way to find the missing side)

If my example is
Town x is 9 miles from town y, and 12 miles from town z. A road connects towns y and z directly. Find the length of this road. 9^2 + 12^2 = c^2

how can i find the length of c using trig. functions? (I know c=15 by using pythagorean theorem)

Thanks
Hi Mandy123,

One must assume that the angle formed at town X to the other two towns is a right angle in order for your solution to work.

One way using trig:

$\tan y=\frac{12}{9}$

$y=\tan^{-1}\left(\frac{12}{9}\right)=53.13010235^{\circ}$

$\sin (53.13010235^{\circ})=\frac{12}{c}$

$c=\frac{12}{\sin (53.13010235^{\circ})}=15$

3. Thank you so much, i was missing the tangent inverse part, and my calculator was in the wrong mode, so thank you so much!!!!