To find the height of a tree, a man stands at point T. His height RT=6 ft. He stands 15 feet from point S and 25 feet from point U. What is the height of the tree, QU?
A.)12 ft
B.)15 ft
C.)16 ft
To find the height of the tree, we can use the concept of similar triangles.
Let's consider two right triangles OQS and ORU, where O is the top of the tree, Q is the top of the man's head, R is where the man is standing, S is a point on the ground directly below Q, and U is a point on the ground directly below O.
In triangle OQS, the side QS represents the man's distance from the tree, which is 15 ft. The side AQ represents the height of the tree, which we want to find.
In triangle ORU, the side RU represents the man's distance from the tree, which is 25 ft. The side AU represents the height of the tree, which we also want to find.
Since the triangles OQS and ORU are similar, their corresponding sides are proportional. This means that we can set up the following proportion:
QS / AQ = RU / AU
Substituting the given values, we have:
15 ft / AQ = 25 ft / AU
To find AU, we can cross-multiply:
15 ft * AU = 25 ft * AQ
Simplifying further:
15 AU = 25 AQ
Dividing both sides by 15:
AU = (25/15) * AQ
Now we know that AU is equal to (25/15) times AQ.
We are given that RT (the man's height) is 6 ft, which is equal to AQ. So, if we substitute 6 ft for AQ, we can solve for AU:
AU = (25/15) * 6 = 10 ft
Therefore, the height of the tree, QU, is 10 ft.
None of the answer choices given match this result, so it seems there might be an error or missing information in the question.