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Tony is standing at sea level. From his location, the angle of elevation of the top of Blue Mountain is 23°. Staying at sea level, he walks 220 yards toward the mountain. The angle of elevation of the top is now 27°. Find the height of Blue Mountain. Round intermediate results to 3 decimal places and the final answer to 1 decimal place.

Respuesta :

Answer:

559.2 yards.

Step-by-step explanation:

Let the height of the mountain be x yards and the distance from the second location to the base of the mountain be y yards.

Then we have the equations:

tan 27 = x/y

tan 23 = x / (220 + y)

From the first equation  y =  x/ tan27 so substituting in the second one we have:

tan 23 =  x / (220 + x / tan 27)

Cross multiply:

x = 220 tan23 +  x tan 23 / tan 27

x =  93.384 + 0.833 x

x - 0.833x = 93.384

x = 93.384 / 0.167

x = 559.2 yards to 1 dec place (answer).

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