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?

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