Question

In triangle AGH, the measure of ∠A = 90°, the measure of ∠G = 31°, and IG = 6.3 feet. Find the length of HI to the nearest tenth of a foot.

Answer 1

Step-by-step explanation:

To find the length of HI in triangle AGH, we can use trigonometry. Since we know the measures of two angles, we can determine the measure of the third angle by subtracting the sum of the other two angles from 180°.

∠A + ∠G + ∠H = 180°

90° + 31° + ∠H = 180°

121° + ∠H = 180°

∠H = 180° - 121°

∠H = 59°

Now that we know the measure of ∠H, we can use the tangent function to find the length of HI. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side.

tan(∠H) = HI / IG

Substituting the known values:

tan(59°) = HI / 6.3

To find HI, we can multiply both sides of the equation by 6.3:

HI = 6.3 * tan(59°)

Using a calculator, we can find the value of tan(59°) to be approximately 1.6643:

HI = 6.3 * 1.6643

HI ≈ 10.47 feet

Therefore, the length of HI in triangle AGH is approximately 10.47 feet to the nearest tenth of a foot.

Answer 2

Using the tangent trigonometric ratio in a right triangle with one angle of 31° and an adjacent side of 6.3 feet, the length of the opposite side HI is calculated to be approximately 3.9 feet to the nearest tenth.

Step-by-step explanation:

The correct answer is option based on the trigonometry and geometry principles involved. Since IG is given as 6.3 feet and the measure of ∠G is 31° in the right triangle AGH, you can use trigonometric ratios to find the length of HI.

The tangent function, which relates the opposite side to the adjacent side in a right triangle, is what we'll use here. The tangent of ∠G equals the length of HI (opposite side) divided by the length of IG (adjacent side).

So,
tan(31°) = HI / 6.3 feet. By solving for HI, you get HI = 6.3 feet * tan(31°). Calculate HI using a calculator set to degree mode to get HI approximately equal to 3.9 feet (rounded to the nearest tenth).