Answer:
Helio is 53.2 feet from the kite ⇒ the last answer
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