A point is directly below a window. Another point B is 15 m from A and at the same horizontal level. From B angle elevation of the top of the bottom of the window is 30° and the angle elevation of the top of the widow is 35°. Calculate the vertical distance
If you want the vertical distance from point A to the bottom of the window you would use the right angled triangle produced by your sketch and find the height using the tangent ratio.
Tan theta = opposite / adjacent
tan30=height/15
Now... if you were actually looking for the distance from the bottom of the window to the top of the window.... it would take a bit more work.
step 1) find the height from A to the bottom of the window (as done above
step 2) use the Pythagorean theorem to find the distance from the bottom of the window to point B
step 3) use the Pythagorean theorem to find the distance from the point B to the top of the window...
step 4) now you have a side angle side triangle and you can use the cosine law to find the distance from the bottom to the top of the window : )
Again... your description in the question was a bit vague and I wasn't sure which distance you were required to find. I would say that if you have already studied the COSINE LAW then it would be the second solution with steps 1-4
An answer
To calculate the vertical distance between the two points, we can use trigonometry.
First, let's label the points:
- Point A is directly below the window.
- Point B is 15 m away from point A at the same horizontal level.
Now, let's break down the problem:
- We have two angles related to the window: 30° and 35°.
- We want to find the vertical distance between the bottom and top of the window.
To tackle this, we'll use the tangent function, which relates the ratio of the opposite side to the adjacent side of a right triangle.
Step 1: Finding the height of the bottom of the window
Using the angle of elevation of the bottom of the window (30°), we can define the equation:
tan(30°) = height of the bottom of the window / distance AB
We can rearrange this equation to solve for the height of the bottom of the window:
height of the bottom of the window = tan(30°) * distance AB
Step 2: Finding the height of the top of the window
Similarly, using the angle of elevation of the top of the window (35°), we can define the equation:
tan(35°) = height of the top of the window / distance AB
We can rearrange this equation to solve for the height of the top of the window:
height of the top of the window = tan(35°) * distance AB
Step 3: Calculating the vertical distance
To find the vertical distance between the bottom and top of the window, we subtract the height of the bottom of the window from the height of the top of the window:
vertical distance = height of the top of the window - height of the bottom of the window
By substituting the values and performing the calculations, you will get the vertical distance.