the angle of elevation from the top of a 16m building to the top of a second building is 48 degrees,
The buildings are 30m apart. What is the height of the taller building?
First let's just look at the right triangle on top. The side adjacent to the 48° angle is 30 m. And we can find the length of the side opposite using tangent.
tan 48° = opposite / 30 Multiply both sides by 30 .
opposite = 30 tan 48°
And....
height of taller tower = 16 + 30 tan 48° ≈ 49.318 m
First let's just look at the right triangle on top. The side adjacent to the 48° angle is 30 m. And we can find the length of the side opposite using tangent.
tan 48° = opposite / 30 Multiply both sides by 30 .
opposite = 30 tan 48°
And....
height of taller tower = 16 + 30 tan 48° ≈ 49.318 m