The angle of elevation from the tip of the shadow to the top of the tree is 36°. Find the distance from the top of the tree to the tip of the shadow. Round the answer to the nearest tenth.
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To solve this problem, we can use a trigonometric function called tangent. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.
Let's call the distance from the top of the tree to the tip of the shadow "x". From the given information, we know that the angle of elevation is 36°. This means that the opposite side of the triangle is the height of the tree, and the adjacent side is the distance from the top of the tree to the tip of the shadow (x).
So, we have the following information:
Angle of elevation = 36°
Opposite side = height of the tree
Adjacent side = x (distance from the top of the tree to the tip of the shadow)
Using the tangent function, we can set up the equation:
tan(36°) = height of the tree / x
Now, we can solve for x by rearranging the equation:
x = height of the tree / tan(36°)
To find the distance from the top of the tree to the tip of the shadow, we need to know the height of the tree. Without that information, we cannot provide a numerical answer.