Airport meteorologists keep an eye on the weather to ensure the safety of flights. One thing they watch is the cloud ceiling, the lowest altitude at which solid cloud is visible. If the cloud ceiling is too low, the planes are not allowed to take off or land.
At night, a meteorologist can find the cloud ceiling by shining a searchlight vertically into the clouds. They measure the angle of elevation to the spot of light on the cloud.

(a) A searchlight located 200 meters from a weather office is turned on. If the angle of elevation to the spot of light on the clouds is 35°, how high is the cloud ceiling?

(b) A meteorologist finds the cloud ceiling is 1000 meters. Given the searchlight is 200 meters from the office, find the angle of elevation.