A searchlight located 200 meters from a weather office is shined directly overhead. If the angle of elevation to the spot of light on the clouds is 35°, how high is the cloud ceiling? Round to the nearest hundredth.
tanThata=h/200
h=200*tan35
Tan35. H
---------- = --------
1. 200
140.04m
To find the height of the cloud ceiling, we can use the tangent function. The tangent of an angle is the ratio of the opposite side to the adjacent side of a right triangle. In this case, the opposite side is the height of the cloud ceiling and the adjacent side is the distance from the searchlight to the weather office, which is 200 meters.
The formula for the tangent is:
tan(angle) = opposite / adjacent
We can rearrange this formula to solve for the height:
opposite = tan(angle) * adjacent
Let's substitute the given values into the equation:
opposite = tan(35°) * 200
Now, we can use a calculator to find the tangent of 35°:
tan(35°) ≈ 0.7002
Substituting this value into the equation:
opposite ≈ 0.7002 * 200
opposite ≈ 140.04
Therefore, the height of the cloud ceiling is approximately 140.04 meters. Rounded to the nearest hundredth, it's 140.00 meters.