Answer: Distance between parent and coach = 24.05m
Step-by-step explanation:
Angle of sight between the coach and the ground(θ) = 38°
Angle of sight between the parent and the ground (θ) = 30°
Height of diving platform = 10m
The horizontal distance(x) between the coach and Melanie :
Tanθ = opp / adj
Tan 38° = 10 / x
x = 10 / 0.7812856
x = 12.79m
The horizontal distance (y) between the parent and Melanie :
Tanθ = opp / adj
Tan 30° = 10 / y
y = 10 / 0.5773502
y = 17.32m
Angle at base of platform between Melanie's coach and her parent = 105°
Distance (a) between coach and parent can be calculated using the cosine rule.
a^2 = x^2 + y^2 - 2bcCosA
Where a, b, c are side lengths and A is the included angle
Therefore,
a^2 = 12.79^2 + 17.32^2 - 2(12.79)(17.32)Cos105°
a^2 = 163.5841 + 299.9824 − (-114.6686)
a^2 = 163.5841 + 299.9824 + 114.6686
a^2 = 578.2351
a = √578.2351
a = 24.046519
a = 24.05m
