Question

Melanie is standing on the 10 m diving platform. Her coach is on the ground to the

left of her, while her parents are on the ground to the right of her. Her coach is
looking at her at an angle of 38° with the ground, while her parents are looking at her
at an angle of 30° with the ground. If the angle at the base of the platform between
Melanie's coach and Melanie's parents is 105°, how far apart are her coach and her parents to the nearest metre?

Answer 1

Answer: Distance between parent and coach = 24.05m

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