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6 June, 10:01

A lifeguard sits in a chair that is 2.3 metres high. She spots a child in trouble in the

water at an angle of depression of 32◦. How far out from the base of the chair is the child?

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  1. 6 June, 10:22
    0
    base = 3.681 metres far

    Step-by-step explanation:

    The following is one way to perform the calculation. It may not be the best way.

    Calculated based on 2 given angles and 1 given side.

    ∠C = 180° - A - B = 1.01229 rad = 58°

    b = a·sin (B) / sin (A) = 4.34028

    c = a·sin (C) / sin (A) = 3.68077

    Area = ab·sin (C) / 2

    = 4.23288

    Perimeter p = a + b + c = 10.32105

    Semiperimeter s = a + b + c/2

    = 5.16053

    Height ha = 2*Area/a

    = 3.68077

    Height hb = 2*Area/b

    = 1.95051

    Height hc = 2*Area/c

    = 2.3

    Median ma = √ (a/2) 2 + c2 - ac·cos (B) = 3.85624

    Median mb = √ (b/2) 2 + a2 - ab·cos (C) = 2.17014

    Median mc = √ (c/2) 2 + b2 - bc·cos (A) = 2.94568
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