Question

From a point 100m from the food of a building the angle of elevation to the building is 18.7 degrees find the height of the building

Answer 1

Explanation:

From a point 100m from the foot of a building the angle of elevation to the building top is 18.7 degrees. Find the height of the building.

Answer 2

`\sf height \approx 33.85 m`

Explanation:

To find the height of the building, we can use trigonometry. The tangent of the angle of elevation (
`\sf \theta`) is equal to the ratio of the height of the building (
`\sf h`) to the horizontal distance from the point to the base of the building (
`\sf d`).

`\sf \tan(\theta) = (h)/(d)`

In this case,
`\sf \theta` is given as 18.7 degrees, and
`\sf d` is given as 100 meters.

Substitute these values into the formula and solve for
`\sf h`:

`\sf \tan(18.7^\circ) = (h)/(100)`

To find
`\sf h`, rearrange the equation:

`\sf h = 100 \cdot \tan(18.7^\circ)`

Now, plug in the values and calculate:

`\sf h \approx 100 \cdot \tan(18.7^\circ)`

Using a calculator:

`\sf h \approx 100 \cdot 0.3384813258`

`\sf h \approx 33.84813258 \, \textsf{meters}`

`\sf h \approx 33.85 \, \textsf{meters ( in 2 d.p.)}`

Therefore, the height of the building is approximately
`\sf 33.85` meters.