Asked by Chuck Bass
Kara and Zach are standing 350 ft apart and see a hot air balloon floating between them in the sky. They measure angles of elevation of 46° and 63°, respectively. What is the distance between Kara and the balloon?
329.8 ft
266.3 ft
331.9 ft
61.6 ft
All Answers 1
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Let x be the horizontal distance from Kara to the balloon and h its height. Then
tan 46° = h/x and tan 63° = h/(350 − x).
So x tan46 = (350 − x) tan63 ⇒ x = 350·tan63/(tan46 + tan63) ≈ 228.9 ft.
The line-of-sight distance from Kara to the balloon is
d = sqrt(x^2 + h^2) = x / cos46° ≈ 228.9 / cos46° ≈ 329.8 ft.
Answer: 329.8 ft.
tan 46° = h/x and tan 63° = h/(350 − x).
So x tan46 = (350 − x) tan63 ⇒ x = 350·tan63/(tan46 + tan63) ≈ 228.9 ft.
The line-of-sight distance from Kara to the balloon is
d = sqrt(x^2 + h^2) = x / cos46° ≈ 228.9 / cos46° ≈ 329.8 ft.
Answer: 329.8 ft.
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