The Washington Monument is 169 meters high. Find the angle of elevation to the nearest degree to the top of the monumenmt from a point .5 km from the base.
looks like
tan Ø = 169/500 = .338
Ø= appr 19°
To find the angle of elevation to the top of the Washington Monument, you can use the tangent function.
First, convert the distance from the base to kilometers to meters:
.5 km = .5 * 1000 meters = 500 meters
Then, we can create a right triangle with the Washington Monument, the point from the base, and the angle of elevation we want to find.
The opposite side of the angle of elevation is the height of the Washington Monument, which is 169 meters.
The adjacent side of the angle of elevation is the distance from the base to the point, which is 500 meters.
Now, we can use the tangent function:
tan(theta) = opposite / adjacent
tan(theta) = 169 / 500
Now, we need to find the angle, theta. To do this, we can take the arctan (inverse tangent) of both sides:
theta = arctan(169 / 500)
Using a calculator or a math tool, we can find:
theta ≈ 19.94 degrees
Therefore, the nearest degree to the angle of elevation to the top of the Washington Monument from a point 0.5 km from the base is approximately 20 degrees.