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?

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Answer 1 · 2017-07-15T07:56:22

$AC = 5.58$ inches

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 $hatA$ this is the adjacent side.
In terms of $hatB$ 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:

$(AC)/4 = tan65" and "(AC)/4 = cot25 = 1/tan25$

$AC = 4 tan65" and "AC= 4cot25 = 4/tan25$

$" "AC = 8.58$ inches

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