## 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**

**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

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

**Step 3**

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

Correct to 4 decimal place for simplicity, hence

**Step 4**

Consider second triangle **ABD **from point** D, so**

**Step 4**

Equate the two equations to* resolve for the unknown x*

Expand the bracket and collect the like terms

From equation 2, the height of building h will be

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