Two buildings are 30m apart. The angle of depression from the top of the taller building to the top of the shorter building is 12 degrees. The height of of the shorter building is 45 m. What is the height of the taller building?
draw the diagram. It should be clear that
(h-45)/30 = tan12°
Now solve for h
Two office buildings are 51 meters apart. The height of the taller building is 207 meters. The angle of depression from the top of the taller building to the top of the shorter building is 15°. Find the height of the shorter building to the nearest meter.
To find the height of the taller building, we can use trigonometry. Let's denote the height of the taller building as h.
Using the angle of depression and the given information, we can form a right triangle. The side opposite the angle of depression is the height of the shorter building (45 m), and the distance between the buildings (30 m) is the adjacent side.
We can use the tangent function to solve for the height of the taller building:
tan(angle) = opposite/adjacent
tan(12 degrees) = 45 m/30 m
tan(12 degrees) = 1.5
To isolate h, we multiply both sides by 30 m:
1.5 * 30 m = h
We find that h = 45 m. Therefore, the height of the taller building is 45 meters.
To find the height of the taller building, we can use trigonometry and the concept of angle of depression.
Let's denote the height of the taller building as "h". We know the height of the shorter building is 45 m.
First, we can calculate the distance between the top of the taller building and the top of the shorter building. Since the buildings are 30m apart, the horizontal distance between them is 30m.
Now, using the angle of depression, which is the angle formed between the horizontal line and the line of sight from the top of the taller building to the top of the shorter building, we can set up a right triangle.
The opposite side of the triangle is the height of the shorter building, which is 45m. The adjacent side is the horizontal distance between the two buildings, which is 30m. And the angle opposite to the side of the shorter building is the angle of depression, which is 12 degrees.
Now, we can use the tangent function to find the height of the taller building. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, we have:
tan(12 degrees) = 45m / 30m
To solve for h, we can rearrange the equation:
h = tan(12 degrees) * 30m
Using a scientific calculator, we can calculate the value of tan(12 degrees):
tan(12 degrees) ≈ 0.2126
Substituting this value back into the equation, we find:
h = 0.2126 * 30m
h ≈ 6.378m
Therefore, the height of the taller building is approximately 6.378 meters.