Question

A helicopter hovers at an altitude that is 1000 feet above a mountain peak of altitude 5250 feet, as shown in the figure. A second, taller peak is viewed from both the mountaintop and the helicopter. From the helicopter, the angle of depression is 43°, and from the mountaintop, the angle of elevation is a = 21º. (Round your answers to the nearest foot.) 430 1000' (a) Approximate the distance from peak to peak. ft (b) Approximate the altitude of the taller peak. ft

Answer 1

briven: a=21 het height of mountain t Alelicopter A 43° - x In ABCD 10oo-h Tan a = feet 43 h x .C Tan 21 - h a B D In ДА СЕ - Tan 43° 2 AG CE Tan43° Loooh

1000 h Tan43° from ean h- Bir Tanat h Tanat 1000h Tan 43° C ST h tan43 Tanat 1000 h

2.4292 h 2000-h 2.4292h the 1000 3.429 2 h = 1000 ha 1000 3.4292 h = 291.61 feet In ABC D sin2i = co Bc BC h Sin24

BC 291.61 Sinal BC = 813-716 BC ² 813.72 feet Hence: Distance from peak to Peak EBC) 813.72 feet a 1814 feet Taller peak altitude - 5250 + 291.64 2 5541.64 1554 15542 feet

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