Question

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?

Answer 1

base= 3.681 metres far

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