Chung-ho is standing on the top of a building that is 135 m talk. The angle of depression to the top of the building next door is 71 degrees. The angle of depression to the basebof the building is 77 degrees. The building are 31 m apart. How talk is the other building?
To find the height of the other building, we can use trigonometric ratios. In this case, we can use the tangent of the angle of depression.
Let's label the height of the other building as 'h'.
1. Find the angle of elevation from the top of the other building to the top of Chung-ho's building:
Since the angle of depression is 71 degrees to the top of the building next door, the angle of elevation from the top of the other building to the top of Chung-ho's building is also 71 degrees.
2. Find the distance from the top of Chung-ho's building to the base of the other building:
Given that the buildings are 31 m apart and Chung-ho's building is 135 m tall, the horizontal distance between the top of Chung-ho's building and the base of the other building can be found using the Pythagorean theorem:
Distance^2 = (31 m)^2 + (135 m)^2
Distance^2 = 961 m^2 + 18225 m^2
Distance^2 = 19186 m^2
Distance ≈ 138.53 m
3. Use the tangent function to find the height of the other building:
tan(angle of elevation) = height of the other building / distance
tan(71 degrees) = h / 138.53 m
4. Solve for the height of the other building:
h = tan(71 degrees) * 138.53 m
Using a calculator, we can find the value of the tangent of 71 degrees and multiply it by 138.53 m to get the height of the other building.