Angle of Elevation and Depression Solved

How to determine height of a building, angle of elevation

Question 1

A contractor measures the angle of elevation of the top of a perpendicular building as 30◦. He then moves 150 m closer to the building and discovers the angle of elevation is raised to 60◦. Determine the height of the building

What is angle of elevation?

It is the angle that the imaginary line or path taken by (object or human) must be raised or elevated from the horizontal (the ground). The contractor is the human, if he walked or moved 150 meter closer to the building, he would have raised or elevated its angle from the ground surface from 30 to 60 degrees.

Solution

angle of elevation and depression

Step 1

Interpret the question with a slight creative illustration, the image shows the building, the movement of the contractor nearer 150 meters towards when he raised it elevation from 30 degrees to 60 degrees. The missing part is to determine the height of the building and how much distance he had to covered on the ground from point C to point B when he stopped at point D.

Step 2

Considering the triangle ABC,  find the angle of elevation from point C

2022 12 16 17h55 35

Remember, tangent = opposite/adjacent

The height of the building is on the opposite and the ground level is on the adjacent side comprise (the unknown x and 150 meter). Rewrite and substitute the values into the formula

2022 12 16 17h57 04

Step 3

The unknown x indicates how much distance the contractor had to cover before getting to the end of the building, so we need to find the unknown distance “x”

2022 12 16 18h03 52

2022 12 16 18h03 16

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Correct to 4 decimal place for simplicity, hence

2022 12 16 18h07 49

Step 4

Consider second triangle ABD from point D, so

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2022 12 16 18h13 12

2022 12 16 18h14 02

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Step 4

Equate the two equations to resolve for the unknown x

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Expand the bracket and collect the like terms

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2022 12 16 18h42 59

2022 12 16 18h43 34

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From equation 2, the height of building h will be

2022 12 16 18h46 29

2022 12 16 18h47 18

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