A building is 50 feet high. At a distance away from the building, an observer notices that the angle of elevation to the top of the building is 41 degrees. How far is the observer from the base of the building?
50/(tan(41)) = x
An airplane is flying at a height of two miles above the ground. The distance along the ground from the airplane to the airport is five miles. What is the angle of depression from the airplane to the airport?
To find the distance from the observer to the base of the building, we can use trigonometry and the concept of tangent.
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.
Did you make your sketch??
If so, then you will see that
tan41° = 50/d
d = 50/tan41
= ....