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From the top of a 292292​-foot ​lighthouse, a plane is sighted​ overhead, and a ship is observed directly below the plane. The angle of elevation of the plane is 2020degrees°​, and the angle of depression of the ship is 3636degrees°. Find a. the distance of the ship from the lighthouse and b. the​ plane's height above the water. Round to the nearest foot.

Respuesta :

Answer

given,

height of the light house = 292 foot

angle of depression of ship = 36°

angle of elevation of plane = 20°

Assuming the height of the plane above tower be 'h'

now

for distance of ship

[tex]tan \theta = \dfrac{P}{B}[/tex]

[tex]tan 36^0 = \dfrac{292}{B}[/tex]

[tex]B = \dfrac{292}{0.727}[/tex]

B= 401. 9 ft

height of the plane

[tex]tan \theta = \dfrac{P}{B}[/tex]

[tex]tan 20^0 = \dfrac{h}{401.9}[/tex]

[tex]h = 401.9 \times 0.364[/tex]

h= 146.28 ft

height of plane from ground = 292 + 146.28

                                                 = 438.28 ft

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