A ramp 38' long rises to a platform. The bottom of the platform is 20' from the foot of the ramp. Find x , the angle of elevation of the ramp. Round your answer to the nearest hundredth of a degree.
After this question I'm done with TRIG!!! Thanks
cos x = 20/38
use your calculator to find x = appr. 58.24°
To find the angle of elevation (x) of the ramp, we can use trigonometry.
First, let's visualize the situation. We have a right triangle, where the length of the ramp represents the hypotenuse, the height of the platform represents the opposite side, and the distance from the foot of the ramp to the platform represents the adjacent side.
Using the trigonometric ratio tangent (tan), we can write the equation:
tan(x) = opposite / adjacent
In this case, the opposite side is the height of the platform, which is 20', and the adjacent side is the distance from the foot of the ramp to the platform, which we'll call "a" for now.
Now, we can substitute these values into the equation:
tan(x) = 20' / a
We need to find the value of "a" to proceed.
To do that, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse is the length of the ramp, which is 38', and the other two sides are the height of the platform (20') and the unknown side "a" (adjacent side).
Using the Pythagorean theorem, we get:
38^2 = 20^2 + a^2
Simplifying this equation:
1444 = 400 + a^2
Subtracting 400 from both sides:
1444 - 400 = a^2
1044 = a^2
Taking the square root of both sides, we find:
a = √1044
Now that we have the value of "a," we can substitute it back into the equation we derived earlier:
tan(x) = 20' / √1044
Using a calculator to find the decimal value of the square root:
a ≈ 32.2803
Now, we can calculate the tangent of x:
tan(x) ≈ 20' / 32.2803
Using a calculator to find the inverse tangent (arctan) of this ratio:
x ≈ arctan(20' / 32.2803)
The approximate value of x is the angle of elevation of the ramp. Round it to the nearest hundredth of a degree for the final answer.