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2 years ago

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

Mathematics

1 answer:

Nookie1986 [14]2 years ago

7 0

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

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