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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.

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Answer:

To find the length of the other leg of a right triangle, we can use trigonometric ratios. In this case, since we know the measure of one angle and the length of the adjacent leg, we can use the trigonometric ratio of the tangent function.

The tangent of an angle is defined as the ratio of the length of the opposite leg to the length of the adjacent leg.

In this problem, the given angle is 30 degrees, and the length of the adjacent leg is 25 inches.

Let's calculate the length of the other leg using the tangent function:

tan(30 degrees) = opposite leg / adjacent leg

tan(30 degrees) = opposite leg / 25 inches

To solve for the opposite leg, we multiply both sides by 25 inches:

opposite leg = 25 inches * tan(30 degrees)

Using a calculator, the tangent of 30 degrees is approximately 0.5774.

opposite leg = 25 inches * 0.5774

opposite leg ≈ 14.435 inches

Rounded to the nearest tenth, the length of the other leg is 14.4 inches.

Therefore, the correct answer is 14.4 in.

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