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3 December, 10:10

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

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  1. 3 December, 12:02
    0
    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
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