Question

5. The distance between two buildings is 67 m. From the top of the shorter building,

the angle of elevation to the top of the taller building is 27°. From the same
position, the angle of depression to the base of the taller building is 39°.
Calculate the height of the two buildings.

Answer 1

To find the heights of the two buildings, use the angles of elevation and depression along with the distance between the buildings to set up trigonometric ratios. The height of the shorter building is approximately 43.07 m and the height of the taller building is approximately 30.63 m.

Step-by-step explanation:

To find the height of the two buildings, we can use trigonometry. Let's start by finding the height of the taller building. We can use the angle of elevation of 27° and the distance between the two buildings of 67 m to set up a trigonometric ratio.

Sin(27°) = Opposite / Hypotenuse

Opposite = Sin(27°) * Hypotenuse

Opposite = Sin(27°) * 67

Opposite ≈ 30.63 m

So, the height of the taller building is approximately 30.63 m.

Next, let's find the height of the shorter building using the angle of depression of 39°.

Sin(39°) = Opposite / Hypotenuse

Opposite = Sin(39°) * Hypotenuse

Opposite = Sin(39°) * 67

Opposite ≈ 43.07 m

Therefore, the height of the shorter building is approximately 43.07 m.