In ΔEFG, the measure of ∠G=90°, the measure of ∠E=40°, and EF = 75 feet. Find the length of GE to the nearest tenth of a foot

19.4 feet

Step-by-step explanation:

Since the triangle has a right angle (as one of the angles in it is equal to 90°), we may find the length of the unknown side using the trigonometric notations SOH CAH TOA where

SOA stands for

Sin Ф = opposite side/hypotenuses side

Cosine Ф = adjacent side/hypotenuses side

Tangent Ф = opposite side/adjacent side

Given that the measure of ∠G=90° and ∠E=40°

EF is the hypotenuse side

FG is the opposite side and

GE is the adjacent side. As such if EF = 75 feet

Cos 75 = GE/75

GE = 75 Cos 75°

= 19.41 feet

≈ 19.4 feet in the nearest tenth of a foot