chung ho is standing on the top of a building that is 135m tall. The angle of depression to the top of the building next door is 71 degrees. The angle to the base of the building is 77 degrees. The buildings are 31m apart. How tall is the other building?
thanks for your help.
(135-h)/31 = tan 71°
h = 44.96
probably use h=45m
135-45 = 90
90/31 = 2.90 = tan 71°
if the height is h,
(135-h)/31 = tan 19°
it doesn't really matter what the angle to the base is, but we'd better have tan 77° = 135/31
ok ty
To find the height of the other building, we can use trigonometry and the concept of angles of depression.
Let's label the height of the other building as "h" meters.
Now, we have two triangles: Triangle A and Triangle B. Triangle A is formed by Chung Ho, the top of the building he's standing on, and the top of the other building. Triangle B is formed by Chung Ho, the top of the building he's standing on, and the base of the other building.
We're given that the angle of depression to the top of the other building is 71 degrees. This means that the angle between Chung Ho's line of sight and the horizontal line is 71 degrees. Similarly, the angle of depression to the base of the other building is 77 degrees.
Let's consider Triangle A first. The bottom angle in Triangle A is 71 degrees (angle of depression) and the top angle is 90 degrees (forming a right angle with the horizontal line). The sum of the angles in a triangle is always 180 degrees, so we can calculate the remaining angle as follows:
Remaining angle in Triangle A = 180 - (90 + 71) = 19 degrees
Now, we know that Triangle A is a right triangle (as one angle is 90 degrees) and the angle opposite to the 135-meter height is 19 degrees. We can use trigonometry (specifically, the tangent function) to find the height of the other building:
tan(19 degrees) = h / 31
tan(19 degrees) = h / 31
To isolate "h" in the equation, we can cross-multiply:
h = 31 * tan(19 degrees)
Using a scientific calculator, we find that:
h ≈ 11.24 meters
Therefore, the other building is approximately 11.24 meters tall.