Did you make your sketch??
If so, then you will see that
tan41° = 50/d
d = 50/tan41
= ....
If so, then you will see that
tan41° = 50/d
d = 50/tan41
= ....
Let's label the distance from the observer to the base of the building as 'x'. We can create a right triangle with the building's height (50 feet), the distance 'x' (which we need to find), and the angle of elevation (41 degrees).
Tangent is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle. In this case, the tangent of the angle of elevation (41 degrees) is equal to the height of the building (50 feet) divided by the distance 'x'.
Using the tangent formula, we have:
tan(41 degrees) = 50 feet / x
Now we can solve for 'x' by rearranging the equation:
x = 50 feet / tan(41 degrees)
Using a calculator, evaluate the tangent of 41 degrees, and then divide 50 feet by that value to find 'x'.
Assuming you have a scientific calculator or a calculator app, perform the following steps:
1. Enter 41 (the angle in degrees).
2. Press the tangent button (tan).
3. Press the equals button (=) to calculate the tangent of 41 degrees.
4. Then divide 50 by the result obtained in step 3.
The final answer will give you the distance 'x' from the observer to the base of the building.