A park is showing a movie on the lawn. The base of the screen is 6 feet off the ground and the screen is 22 feet high (see figure in the link below).
www.webassign.net/larprecalcrmrp6/4-8-047.gif
(b) You are lying on the ground and the angle of elevation to the top of the screen is 35°. How far are you from the screen? (Round your answer to two decimal places.)
Much ado about nothing,
The top of the screen is 28 ft above the ground
let your distance from the screen be x
So we just have tan 35 = 28/x
x = 28 / tan35 = ....
To calculate the distance from the screen, we can use trigonometry. Let's refer to the distance from you to the screen as "x".
In the given figure, the angle of elevation to the top of the screen is 35°. This means that if we were to draw a line from your eyes to the top of the screen, it would form a right triangle.
To find the distance "x", we can use the tangent trigonometric function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle.
In this case, the opposite side is the height of the screen (22 feet) and the adjacent side is the distance "x" from you to the screen.
Therefore, we can set up the following equation:
tan(35°) = opposite/adjacent
tan(35°) = 22/x
Now, we can solve for "x" by rearranging the equation:
x = 22 / tan(35°)
Using a calculator, we can evaluate the tangent of 35° and calculate "x":
x ≈ 22 / 0.7002
x ≈ 31.41 feet
Therefore, you are approximately 31.41 feet away from the screen.
To find the distance from you to the screen, we can use trigonometry and the given information.
Let's denote the distance from you to the screen as "d".
We have the angle of elevation to the top of the screen as 35°.
We can use the tangent function:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the screen (22 feet) and the adjacent side is the distance from you to the screen (d).
So, we have:
tan(35°) = 22/d
To solve for "d", we can rearrange the equation:
d = 22/tan(35°)
Calculating this using a calculator, we find:
d ≈ 22/0.7002
d ≈ 31.41 feet
Therefore, you are approximately 31.41 feet away from the screen.