Ryan places a mirror on the ground 42 feet from the base of a tree. He walks backwards until he can see the top of the tree in the middle of the mirror. At that point, Jason's eyes are 6 feet above the ground and he is 7 feet from the image in the mirror. What is the height of the tree?A.39 feetB.56 feetC.49 feetD.36 feet
Question
Ryan places a mirror on the ground 42 feet from the base of a tree. He walks backwards until he can see the top of the tree in the middle of the mirror. At that point, Jason's eyes are 6 feet above the ground and he is 7 feet from the image in the mirror. What is the height of the tree?A.39 feetB.56 feetC.49 feetD.36 feet
Solution
This problem can be solved using similar triangles.
The first triangle is formed by Ryan, the mirror, and the image of the top of the tree in the mirror. The second triangle is formed by the mirror, the base of the tree, and the top of the tree.
Since the triangles are similar, the ratios of corresponding sides are equal.
Let's denote the height of the tree as h.
The ratio of the height to the distance from the mirror is the same in both triangles. So, we can set up the following equation:
6/7 = h/42
To solve for h, we multiply both sides by 42:
h = 6 * 42 / 7 = 36
So, the height of the tree is 36 feet.
The correct answer is D. 36 feet.
Similar Questions
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