Question

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?

Answer 1

Answer:

A

C

=

5.58

inches

Step-by-step explanation:

Label the vertices of the triangle as ABC.

Fill in all the angles.

ˆ

A

=

25

°

,

ˆ

C

=

90

°

,

∴

ˆ

B

=

65

°

The side you are looking for is AC.

In terms of  

ˆ

A

this is the adjacent side.

In terms of  

ˆ

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

=

adj

opp

=

1

tan

)

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

Compare the following equations:

A

C

4

=

tan

65

         and        

A

C

4

=

cot

25

=

1

tan

25

A

C

=

4

tan

65

         and        

A

C

=

4

cot

25

=

4

tan

25

     

A

C

=

8.58

inches