Question

In triangle HIJ, the measure of angle J equals 90 degrees, HI equals 8 feet, and JH equals 1.9 feet. Find the measure of angle H to the nearest tenth of a degree.

A. 15.7 degrees

B. 74.3 degrees

C. 105.6 degrees

D. 165.4 degrees

Answer 1

To find the measure of angle H in right-angled triangle HIJ, we use the tangent function tan(H) = opposite/adjacent = 1.9/8. Taking the inverse tangent results in angle H ≈ 13.4 degrees, which suggests a typo or error in the provided options.

Step-by-step explanation:

The problem asks us to find the measure of angle H in a right-angled triangle HIJ. Since angle J is 90 degrees, angle H and angle I must add up to 90 degrees as well (since the sum of the angles in a triangle is always 180 degrees). To find the measure of angle H, we can use the trigonometric function known as the tangent (tan), which is the ratio of the opposite side over the adjacent side in a right-angled triangle.

Here, for angle H, the opposite side is JH (1.9 feet) and the adjacent side is HI (8 feet). So, we have:

• tan(H) = opposite/adjacent = JH/HI = 1.9/8

To find the measure of angle H, we can take the inverse tangent (tan-1) of this ratio:

• angle H = tan-1(1.9/8)

By calculating the inverse tangent, we find that:

• angle H ≈ 13.4 degrees (rounded to the nearest tenth)

This measure does not match with any of the given options A-D precisely, suggesting a typo in those options or a calculation error. According to the trigonometric calculation, perhaps option A. 15.7 degrees is the closest to the calculated angle, if we account for possible rounding differences or typographical errors in the problem statement or the options provided.