Question

A platform and a building are on the same horizontal plane the angle of depression of the bottom C of the building from the top A of the platform is 39°.The angle of the elevation of the top of the top D of the building from the top of the platform is 56°.Given that the distance between the top of the platform and that of the building is 10m.Calculate the height of the building to the nearest whole number?

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Answer 1

Answer: Let's draw a diagram to visualize the problem:

C D

| |

|h |

| |

|_ _ _ |_ _ _ _ _ _

A 10m B

In the diagram, A represents the top of the platform, B represents the bottom of the building, C represents the bottom of the building as seen from the top of the platform, D represents the top of the building as seen from the top of the platform, h represents the height of the building, and the angles of depression and elevation are labeled.

We can use trigonometry to solve for h. Let x be the distance from point A to point C, as shown in the diagram. Then we have:

tan(39°) = h/x (1)

tan(56°) = (h + 10)/x (2)

We can rearrange equation (1) to get:

x = h/tan(39°)

Substituting this into equation (2), we get:

tan(56°) = (h + 10)/(h/tan(39°))

Simplifying this expression, we get:

tan(56°) = (h + 10)tan(39°)/h

Multiplying both sides by h, we get:

h tan(56°) = (h + 10)tan(39°)

Expanding the right side, we get:

h tan(56°) = h tan(39°) + 10 tan(39°)

Subtracting h tan(39°) from both sides, we get:

h (tan(56°) - tan(39°)) = 10 tan(39°)

Dividing both sides by (tan(56°) - tan(39°)), we get:

h = 10 tan(39°) / (tan(56°) - tan(39°))

Using a calculator to evaluate this expression, we get:

h ≈ 17.5 meters

Therefore, the height of the building is approximately 18 meters to the nearest whole number.