Final answer:
To approximate the measure of angle JGH, the cosine ratio is used, and after calculation, the approximate measure of angle JGH is found to be 70.5°.
Step-by-step explanation:
To find the approximate measure of angle JGH in triangle GJH where GH is the hypotenuse measuring 6 cm, and JH measures 2 cm, we can use trigonometric ratios. Specifically, the cosine of angle JGH can be found using the formula cos(θ) = adjacent/hypotenuse, where the adjacent side to angle JGH is JH (which measures 2 cm) and the hypotenuse GH measures 6 cm.
Calculating the cosine, we get:
cos(JGH) = 2 cm / 6 cm = 1/3
Using a calculator in degree mode, we can then find the angle JGH by calculating the inverse cosine (also known as arccos) of 1/3:
angle JGH ≈ arccos(1/3)
angle JGH ≈ 70.5 degrees
Therefore, the approximate measure of angle JGH is 70.5°.