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.

14.4 in.
21.7 in.
28.9 in.
43.3 in.

Answer 1

If the right triangle has an angle of 30, then the three angles in the triangle must be 30, 60, and 90 degrees. The sides of a 30-60-90 triangle have the ratio 1 : 2 : sqrt(3). The side adjacent to the 30-degree angle is opposite the 60-degree angle, so it has the ratio of sqrt(3). The other leg is opposite the 30-degree angle so it has the ratio 1. The length of the leg we want to find is then (1/sqrt(3)) * 25 inches and 25 / sqrt(3) = 14.4 inches, which is the answer.

Answer 2

The length of the other leg is 14.4 inches

Right triangle

Right triangle are triangle that has one of its angle as 90 degrees. Therefore,

Using trigonometric ratio let's find the other leg

• tan ∅ = opposite / adjacent

tan 30° = x / 25

x = 25 ×  tan 30°

x = 25 × 0.57735026919

x = 14.4337567297

Therefore, the other leg is 14.4 inches

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