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20 February, 22:14

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.

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  1. 20 February, 22:18
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    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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