A cable that is used to support a 76 foot tower is secured to the ground 31 feet from the base of the tower. Find the angle of elevation to the nearest degree that the cable makes with the ground. Answer choices: 22 degrees, 24 degrees, or 68 degrees.
Use tan(angle)= 76/31
which is greater than 1, so the angle must be greater than 45 degrees. there is only one choice greater than 45 degrees.
ok its more than 45 degrees
To find the angle of elevation of the cable, we can use trigonometry.
Let's consider the triangle formed by the cable, the tower, and the ground.
We have the opposite side (the height of the tower) as 76 feet and the adjacent side (the distance from the base of the tower to the point where the cable is secured) as 31 feet.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle.
Using the tangent function, we can calculate the angle of elevation:
tan(angle) = opposite/adjacent
tan(angle) = 76/31
Now, we can solve for angle by taking the inverse tangent (arctan) of both sides:
angle = arctan(tan(angle)) = arctan(76/31)
Using a calculator, we find that the angle is approximately 68 degrees.
Therefore, the correct answer is 68 degrees.