17. farimah and helio are standing 15 ft. apart from each other and looking up at a kite that is with the flying between them. farimah is flying the kite on a 57 ft. string at an angle of 68 ground. how far is helio from the kite? 64.1 ft. 56.2 ft 60.0 ft. 53.2 ft.

Helio is 53.2 feet from the kite ⇒ the last answer

Step-by-step explanation:

* Lets change this story problem to a trigonometry problem

- Assume that there is a triangle joining between the

 kite, Farimah and Helio

- The name of the triangle is KFH, where K position of the kite,

 F position of Farimah and H is the position of Helio

∵ Farimah and Helio are standing 15 feet apart from each other

∴ FH = 15 feet

∵ Farimah is flying the kite on a 57 feet string at an angle

 of 68 with the ground

∴ FK = 57 feet

∴ m∠KFH = 68°

∵ We need to know that Helio is how far from the kite

∴ We need to calculate the length of KH

* Now lets find the best way to find the length of KH

 using the trigonometry

- We have the length of two sides and the measure of the included

 angle between them , then the best way is the cosine Rule

* Lets explain the cosine rule:

- In ΔABC:

∵ a is the length of the side opposite to ∠A ⇒ a is BC

∵ b is the length of the side opposite to ∠B ⇒ b is AC

∵ c is the length of the side opposite to ∠C ⇒ c = AB

∴ a² = b² + c² -2bc × cos(A)

∴ b² = a² + c² -2ac × cos(B)

∴ c² = a² + b² -2ab × cos(C)

* We will use the rule in our problem to find HK

∵ FH is k , HK is f , KF is h

∴ f² = h² + k² - 2hk × cos(F)

∵ h = 57 feet , k = 15 feet , m∠F = 68°

∴ f² = (57)² + (15)² - 2(57)(15) × cos(68) = 2833.4227

∴ f = √2833.4227 = 53.2 feet

* Helio is 53.2 feet from the kite

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step-by-step explanation:

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