1. ## ACT Math Help

I'm studying for the math section of the ACT and I can't remember how to solve this problem.

A right triangle has legs of length 25 sin theta feet and 25 cos theta feet for some angle theta that satisfies 0< theta< 90. What is the length, in feet, of the longest side of the triangle?

F. theta
G. 1
H. 5
J. 25
K. Cannot be determined from the given information

I know that the answer is J but I wasn't given an explanation. If someone could help me that would be great.

2. Hello 5441lk
Originally Posted by 5441lk
I'm studying for the math section of the ACT and I can't remember how to solve this problem.

A right triangle has legs of length 25 sin theta feet and 25 cos theta feet for some angle theta that satisfies 0< theta< 90. What is the length, in feet, of the longest side of the triangle?

F. theta
G. 1
H. 5
J. 25
K. Cannot be determined from the given information

I know that the answer is J but I wasn't given an explanation. If someone could help me that would be great.
If the longest side is $\displaystyle x$, using Pythagoras' Theorem:

$\displaystyle x^2 = (25\sin\theta)^2+(25\cos\theta)^2$

$\displaystyle =25^2\sin^2\theta+25^2\cos^2\theta$

$\displaystyle =25^2(\sin^2\theta+\cos^2\theta)$

$\displaystyle =25^2 \times 1$, using the well-known rule: $\displaystyle \sin^2\theta+\cos^2\theta=1$, for all values of $\displaystyle \theta$

$\displaystyle \Rightarrow x = 25$