Question

A triangle has a hypotenuse of length 25 and one leg of length 24. What is the tangent of the larger acute angle of the triangle?

Answer 1

Answer:

$\sin( \theta) = \frac{24}{25} \\ \theta = { \sin }^{ - 1} ( \frac{24}{25} ) \\ \theta = 73.7 \degree \\ \\ \tan( \theta) = \tan(73.7 \degree) \\ = 3.4$

Answer 2

24 ft
Explanation:
The Pythagorean theorem states that the sum of the squares of the two legs is equal to the hypotenuse squared.
7
2
+
x
2
=
25
2
→
I'll use x to represent the unknown leg.
49
+
x
2
=
625
x
2
=
576
x
=
±
24
→
Eliminate the -24 answer choice; a side length cannot be negative
The other leg is 24 ft.