A person measures the height of a building by walking out a distance of 44.2 m f

Question

A person measures the height of a building by walking out a distance of 44.2 m from its base and shining a flashlight beam toward the top. When the beam is elevated at an angle of 44.4° with respect to the horizontal, as shown in the figure, the beam just strikes the top of the building. Find the height of the building and the distance the flashlight beam has to travel before it strikes the top of the building. (The flashlight is still 2.00 m above the ground.)

While standing atop a building 48.5 m tall, you spot a friend standing on a street corner. Using a protractor and a dangling plumb bob, you find that the angle between the horizontal and the direction to the spot on the sidewalk where your friend is standing is 23.1°. Your eyes are located 1.69 m above the top of the building. How far away from the foot of the building is your friend?

Explanation / Answer

1)
Tan44.4 = height / 44.2

height = Tan44.4 * 44.2 m = 43.28

c = sqrt(a^2 + b^2)

= sqrt((43.28)^2 + (44.2)^2)

so, distance c = 61.86 m

2)
tan[23.1º] = h x

tan[23.1º] = (48.5 + 1.69) x

x = 117.668 meters ... horizontal displacement from building

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