Questions: A right triangle has a hypotenuse of length 2 inches. If one angle is 32 degrees, find the length of each leg. The length of the shorter leg is square inches, and the longer leg is square inches. (Do not round until the final answer. Then round to the nearest tenth as needed.)

A right triangle has a hypotenuse of length 2 inches. If one angle is 32 degrees, find the length of each leg.

The length of the shorter leg is square inches, and the longer leg is square inches.
(Do not round until the final answer. Then round to the nearest tenth as needed.)

Transcript text: A right triangle has a hypotenuse of length 2 inches. If one angle is $32^{\circ}$, find the length of each leg. The length of the shorter leg is $\square$ inches, and the longer leg is $\square$ inches. (Do not round until the final answer. Then round to the nearest tenth as needed.)

Solution

Solution Steps

Step 1: Identify the known values

The length of the hypotenuse (H) is given as 2 units, and the measure of the non-right angle ($\theta$) is 32 degrees.

Step 2: Use trigonometric relationships to find the lengths of the legs

The length of the leg opposite to the angle $\theta$ can be found using the sine function: $Opposite = H \times \sin(\theta)$. Substituting the given values: $Opposite = 2 \times \sin(32) = 1.1$ units. Similarly, the length of the adjacent leg can be found using the cosine function: $Adjacent = H \times \cos(\theta)$. Substituting the given values: $Adjacent = 2 \times \cos(32) = 1.7$ units.