# Given a right triangle with Angle A=25 deg, Angle C=90 Degrees, and knowing the length of the leg opposite angle A equals 4 inches, how do I find the length of the base leg of the triangle?

Jul 15, 2017

$A C = 5.58$ inches

#### Explanation:

Label the vertices of the triangle as ABC.
Fill in all the angles.

hatA = 25°, hatC = 90°, :. hatB= 65°

The side you are looking for is AC.

In terms of $\hat{A}$ this is the adjacent side.
In terms of $\hat{B}$ it is the opposite side.

We have an opposite and an adjacent side, so we will use the Tan or Cot ratio. (If you are unfamiliar with cot, $\cot = \text{adj"/"opp} = \frac{1}{\tan}$)

Tan is a preferred ratio because it is on a scientific calculator, while Cot is not.

Compare the following equations:

$\frac{A C}{4} = \tan 65 \text{ and } \frac{A C}{4} = \cot 25 = \frac{1}{\tan} 25$

$A C = 4 \tan 65 \text{ and } A C = 4 \cot 25 = \frac{4}{\tan} 25$

$\text{ } A C = 8.58$ inches

Both will give the same answer for AC, but the first one is simpler.