Frank A. answered • 07/29/20
A quarter century of teaching IB, GCSE, AP physics and pharmacy math.
Hello Eva C,
Two buildings on opposite sides of the street are 70 meters apart. From the top of the taller building, which is 200 meters high, the angle of depression to the top of the shorter building is 10 degrees. Find the height of the shorter building to the nearest meter.
In the diagram above, the the base of the triangle is the separation between the buildings = 70m
The vertical side of the triangle represents the difference in heights of the two buildings.
Since the angle of depression is given as 10°, we can apply the ratio called tangent θº where θº = 10
tan 10º = perp/base; or 0.18 x 70 = perp = 12.34m
This is the difference in the heights of the two buildings so the shorter building is 200-12.34 = 187.66 m
Reduced to the nearest meter we get 188 m
If you need further clarification, please let me know.
If you, or someone you know, needs one-on-one help with math or physics, keep me in mind.
Mr. A (Frank Ansari)
