A student five and a half feet tall stands opposite of a mirror from a flagpole. The distance between the student and the mirror is 6 feet and the distance from the mirror to the flagpole is 14 feet. What is the height of the flagpole?​

You have decided to go camping with some friends. While out on a hike, you reach the top of a ridge and look down at the trail behind you. In the distance, you can see your camp. You're thinking about how far you've traveled, and wonder if there is a way to determine it.

By using a small device called a clinometer, you're able to measure the angle between your horizontal line of sight and the camp as 37∘, and you know that the hill you just hiked up has a height of 300 m. Is it possible to find out how far away your camp is using this information? (Assume that the trail you hiked is slanted like the side of a triangle.)