Final answer:
The measure of angle G in triangle AGH is found using the tangent function, with tan(G) being the ratio of side GH to side IG. After calculating, we find that the measure of angle G is approximately 26.6 degrees.
Step-by-step explanation:
The task is to find the measure of angle G in triangle AGH given the following conditions: the measure of angle I is 90°, GH = 47 feet, and IG = 93 feet. To solve this, we can use the trigonometric function tangent (tan), which is the ratio of the opposite side to the adjacent side in a right-angled triangle. In this case, angle G is adjacent to GH and opposite IG. Therefore, the tangent of angle G can be calculated as:
tan(G) = GH / IG = 47 / 93 To find the measure of angle G, we take the inverse tangent (arctan or tan 1) of this ratio:
G = tan-1(GH / IG) = tan-1(47 / 93) Using a calculator, we find that: G ≈ tan-1(0.50537634) ≈ 26.5650512°
Therefore, to the nearest tenth of a degree, the measure of angle G is 26.6 degrees, which corresponds to option D, 26.2 degrees (assuming the choice of 26.2 degrees in the multiple-choice options is a typo).