Question

From the top of a building, the angle of elevation to the top of a nearby building is 28° and the angle of depressions to the bottom of the nearby building is 48°. The distance between the two buildings is 50m, as shown in the diagram below. What is the height of the taller building, to the nearest tenth of a metre?

Answer 1

Answer:

Step-by-step explanation:

The idea here is to find the value for x and y, then add them together. See the pic I attached below. We will solve for side x first.

Side s is across from the reference angle of 48 degrees; side measuring 50 m is adjacent to the reference angle 48 degrees. Therefore, we will use the tangent ratio to solve for x:

$tan48=\frac{x}{50}$ and

50tan(48) = x so

x = 55.53m

Now we will do the same and solve for y. This time the reference angle is 28 degrees. Side y is opposite the reference angle and the side measuring 50 is adjacent to the reference angle, so we will use the tangent ratio again:

$tan28=\frac{y}{50}$ and

50tan(28) = y so

y = 26.59. Therefore,

x + y = 55.53 + 26.59 and

the height of the taller building is

82.1 m