The shadow of a vertical tower is 65 ft long when the angle of elevation of the sun is 35 degrees. Find the height of the tower
Find the angle of elevation of the sun when a tower 83 m high casts a shadow 20 m long.
Application of surds in solving triangles(trigonometrical ratios of special triangles)calculate the height of a tree whose shadow is 20m shorter when the angle of elevation of the sun is 60° than when the angle of elevation is 30°
To find the height of the tower, we can use trigonometry and the given information. Let's break down the problem:
1. The shadow of the tower is 65 ft long.
2. The angle of elevation of the sun is 35 degrees.
We can use the tangent function to find the height of the tower.
1. Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the height of the tower (let's call it "h") and the adjacent side is the shadow length of 65 ft.
2. The tangent of the angle of elevation (35 degrees) is given by the formula:
tan(angle) = opposite / adjacent
tan(35) = h / 65
3. To solve for the height of the tower, we can rearrange the formula:
h = 65 * tan(35)
Plugging in the values and using a calculator, we can find the height of the tower:
h = 65 * tan(35)
h ≈ 65 * 0.7002
h ≈ 45.5097 ft
Therefore, the height of the tower is approximately 45.51 ft.
clear case of right-triangle trig
height/65 = tan 35°
height = 65tan35°
= ....