A surveyor measures the distance between buildings X and Y as 200 feet. The angle of elevation from the base of X to the top of Y is 25 degrees. What is the height of building Y?
Draw a right triangle with XY vertical, and a base AX of 200 ft.
The angle XAY=25 degrees.
Use the definition of
tangent(A)=tangent(25°)=XY/AX
Solve for XY.
To find the height of building Y, we can use trigonometry. Let's denote the height of building Y as h.
We have the distance between buildings X and Y as 200 feet and the angle of elevation from the base of X to the top of Y as 25 degrees.
The trigonometric function that relates the angle of elevation, the opposite side (height in this case), and the adjacent side (distance in this case) is tangent (tan).
In this scenario, we have:
tan(25 degrees) = height (h) / distance (200 feet)
Now we can solve for h by rearranging the equation:
height (h) = tangent(25 degrees) * distance (200 feet)
To calculate the tangent of an angle, you can use a scientific calculator or an online trigonometric calculator.