Question

In right triangle GHI, ∠H is a right angle, m∠I=42∘, and GH=11. sin42∘≈0.67 cos42∘≈0.74 tan42∘≈0.90 Triangle G H I has segment G H that measures 11 units. Angle H is a right angle and angle I is 42 degrees. © 2019 StrongMind. Created using GeoGebra. What is the measurement of HI? If necessary, round your answer to two decimal places, like this: 42.53

Answer 1

To determine the length of HI in the right triangle GHI, use the sine of angle I (sin(42°) which equates to 0.67) and multiply it by the hypotenuse GH (11 units). The resulting length of HI is approximately 7.37 units.

Step-by-step explanation:

To find the measurement of HI in right triangle GHI, where ∠H is a right angle, m∠I=42°, and GH=11, we can use the sine function. Since sin(42°) ≈ 0.67, and GH represents the hypotenuse in this triangle, we can set up the following equation: sin(42°) = HI / GH, which gives us HI = GH * sin(42°). Plugging in the given values, HI = 11 * 0.67.

HI ≈ 7.37 units. So, the measurement of HI is approximately 7.37 units, rounded to two decimal places.