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18 February, 06:18

In ΔTUV, the measure of ∠V=90°, VT = 64 feet, and UV = 43 feet. Find the measure of ∠U to the nearest tenth of a degree.

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  1. 18 February, 08:29
    0
    47.8°

    Step-by-step explanation:

    Let's first outline the important parameters

    -- -
    Vt = 64

    UV = 43

    The angles in a triangle sums up to 180, but we don't have up to 2 angles given so as to find the third one. What we have to is to find the second angle, in this case T, using the sine rule.

    Sin v/v = sin t/t

    (Sin 90) / 64 = sin t/43

    Cross multiply and we have

    43 sin 90 = 64 sin t

    Sin t = 43 sin 90 : 64

    Sin t = 0.6719

    Sine inverse of t = 42.2° (the second angle)

    Angle U = 180 - (90 + 42.2)

    180 - 132.2

    = 47.8°
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