From a window of a building A, the angle of elevation of the top of building B is 35 degrees and the angle of depression of the bottom of building B is 20 degrees. If the buildings are 25m. horizontally apart, Compute for height of the window from the ground? And compute for height of Building B?
Let H be the window height, and X = 25 X = 25 m be the separation of buildings.
L tan20 = H
H = 9.10 m
Building B height = H + L tan 35
= 9.10 + 17.51 = 26.61 m
Draw yourself a figure and these relationships sould be obvious to you.
To compute for the height of the window from the ground, we can use the concept of trigonometry. Here's how:
1. Let's assume the height of the window from the ground is 'h' meters.
2. From the window of building A, the angle of depression of the bottom of building B is 20 degrees. This means that the angle formed between the horizontal line (ground level) and the line of sight from the window to the bottom of building B is 20 degrees.
3. Using the tangent function, we can write the equation as follows: tan(20 degrees) = h / 25 meters.
4. Rearranging the equation, we have h = 25 meters * tan(20 degrees).
5. Use a calculator to find the value of tan(20 degrees) and multiply it by 25 meters to get the height of the window from the ground.
To compute for the height of building B, we can use the concept of trigonometry again. Here's how:
1. Let's assume the height of building B is 'H' meters.
2. From the window of building A, the angle of elevation of the top of building B is 35 degrees. This means that the angle formed between the horizontal line (ground level) and the line of sight from the window to the top of building B is 35 degrees.
3. Using the tangent function, we can write the equation as follows: tan(35 degrees) = H / 25 meters.
4. Rearranging the equation, we have H = 25 meters * tan(35 degrees).
5. Use a calculator to find the value of tan(35 degrees) and multiply it by 25 meters to get the height of building B.
Finally, to summarize:
- The height of the window from the ground is h meters (compute it using h = 25 meters * tan(20 degrees)).
- The height of building B is H meters (compute it using H = 25 meters * tan(35 degrees)).