Question

In ΔEFG, the measure of ∠G=90°, GF = 33, FE = 65, and EG = 56. What ratio represents the sine of ∠F?

Answer 1

To find the sine of ∠F in triangle EFG, use the Pythagorean theorem to find the length of the side opposite ∠F and then calculate the sine using the formula opposite/hypotenuse.

Step-by-step explanation:

To find the sine of ∠F in triangle EFG, we first need to determine the lengths of the sides opposite and adjacent to ∠F. Given that ∠G = 90°, GF = 33, FE = 65, and EG = 56, we can use the Pythagorean theorem to find the length of the side opposite ∠F. Applying the formula a^2 + b^2 = c^2, we have GF^2 + FE^2 = GE^2. Substituting the given values, we get 33^2 + 65^2 = GE^2. Simplifying, we find GE ≈ 72.41.

Now, we can calculate the sine of ∠F using the formula opposite/hypotenuse. Thus, sin∠F = FE/GE = 65/72.41 ≈ 0.897.