Final answer:
To find the measure of ∠H in triangle ΔGHI, use the tangent function with the opposite side (HI) and the adjacent side (GH) to calculate arctan(20/21), resulting in an angle of approximately 44° when rounded to the nearest degree.
Step-by-step explanation:
You've been asked to find the measure of ∠H in a right triangle ΔGHI, where the measure of ∠I is 90°, GH measures 21 feet, and HI measures 20 feet. To find the measure of ∠H, we can use the trigonometric function tangent, which is the ratio of the opposite side to the adjacent side in a right triangle.
Given that HI is the side opposite ∠H and GH is the hypotenuse, we can write the following equation using the tangent function:
tan(∠H) = (opposite side) / (adjacent side)
tan(∠H) = HI / GH
tan(∠H) = 20 / 21
Using a calculator, we can now find the angle ∠H by calculating the inverse tangent (arctan) of (20/21).
∠H = arctan(20/21)
∠H ≈ 43.6° when rounded to the nearest degree.
Therefore, the measure of ∠H is approximately 44°.