at one point in the day, a tower that is 150 feet high casts a shadow that is 210 feet long. Find, to the nearest tenth of a degree, the angle of elevation of the sun at that point
if tanØ = 150/210
Ø = appr 35.5°
To find the angle of elevation of the sun, we can use the tangent function, which relates the height and length of a right triangle to one of its acute angles.
In this case, the tower represents the height of the triangle, and the shadow represents its base. Therefore, we need to find the inverse tangent (arctan) of the ratio of the height to the base.
Step 1: Identify the values given:
- The height of the tower is 150 feet.
- The length of the shadow is 210 feet.
Step 2: Set up the equation:
Let x be the angle of elevation.
We can establish the following relationship based on the tangent function:
tan(x) = height/base
Step 3: Substitute the given values:
tan(x) = 150/210
Step 4: Solve for x:
To find the angle, we need to take the arctan (inverse tangent) of both sides of the equation:
x = arctan(150/210)
Step 5: Calculate:
Using a calculator, evaluate arctan(150/210) ≈ 38.475 degrees.
Therefore, to the nearest tenth of a degree, the angle of elevation of the sun at that point is approximately 38.5 degrees.