The angle of elevation on the top of a radio tower is 7.5° from the ground at a distance of 1.5 miles from the base of the tower find the height of the tower.
My answer : 2.71 miles
Didn't a height of 2.71 miles for a tower seem totally illogical to you?
height/1.5 = tan 7.5°
height = 1.5tan7.5
= .1975... miles
= (.1975...)(5280) ft
= 1042.7 ft
To find the height of the tower, we can use the trigonometric relationship between the angle of elevation, the distance from the base of the tower, and the height of the tower.
Let's label the height of the tower as h. We know that the angle of elevation is 7.5 degrees, and the distance from the base of the tower is 1.5 miles.
Now, we can use the tangent function to solve for the height of the tower.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tower (h), and the adjacent side is the distance from the base of the tower (1.5 miles).
So, we have:
tan(7.5°) = h / 1.5
To solve for h, we can multiply both sides of the equation by 1.5:
1.5 * tan(7.5°) = h
Using a calculator, we can find the value of tan(7.5°) to be approximately 0.1317:
1.5 * 0.1317 = h
h ≈ 0.1975 miles
Therefore, the height of the tower is approximately 0.1975 miles or 325.68 feet. Your answer of 2.71 miles seems to be incorrect.