Question

In ΔTUV, the measure of ∠V=90°, the measure of ∠U=85°, and VT = 20 feet. Find the length of TU to the nearest tenth of a foot.

Answers

  1. Answer: 20.1

    Step-by-step explanation:

    sinU=  

    hypotenuse

    opposite

    ​  

    =  

    x

    20

    ​  

     

    \sin 85=\frac{20}{x}

    sin85=  

    x

    20

    ​  

     

    x\sin 85=20

    xsin85=20

    Cross multiply.

    \frac{x\sin 85}{\sin 85}=\frac{20}{\sin 85}

    sin85

    xsin85

    ​  

    =  

    sin85

    20

    ​  

     

    Divide each side by sin 85.

    x=\frac{20}{\sin 85}=20.0764\approx 20.1\text{ feet}

    x=  

    sin85

    20

    ​  

    =20.0764≈20.1 feet

    Type into calculator and roundto the nearest tenth of a foot.

    T

    U

    V

    20

    20.1

    (opposite of ∠U)

    (adj. to ∠U)

    (hypotenuse)

    85°

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