Question

A right triangle has a 30o angle. The leg adjacent to the 30o angle measures 25 inches What is the length of the other leg? Round to the nearest tenth

Answer 1

Check the picture below

make sure your calculator is in Degree mode.

Answer 2

Answer:  The length of the other leg is 14.43 inches.

Step-by-step explanation:  As shown in the attached figure below, triangle ABC is a right-angled triangle, where

∠ABC = 90°, ∠ACB = 30° and BC = 25 inches.

We are to find the length of the other leg, i.e., the length of AB.

Applying tangent ratio for angle ACB in triangle ABC, we have

$\tan\angle ACB=\dfrac{perpendicular}{base}\\\\\\\Rightarrow \tan 30^\circ=\dfrac{AB}{BC}\\\\\\\Rightarrow AB=\tan30^\circ\times 25\\\\\Rightarrow AB=\dfrac{1}{\sqrt3}\times 25\\\\\\\Rightarrow AB=\dfrac{25}{1.732}\\\\\Rightarrow AB=14.43~\textup{inches}.$

Thus, the length of the other leg is 14.43 inches.