A bamboo pole is leaning against a tree. If the height of the tree is 15.2 meters and the angle made by the pole and the ground is 50°, what is the length of the pole?
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A bamboo pole is leaning against a tree. If the height of the tree is 15.2 meters and the angle made by the pole and the ground is 50°, what is the length of the pole?
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To solve this problem, we can use trigonometry.
First, let's draw a diagram to help us visualize the problem. Let's label the height of the tree as "h" and the length of the bamboo pole as "x". We know that the angle made by the pole and the ground is 50 degrees.
[Diagram: A right triangle with a vertical side labeled "h", a horizontal side labeled "x", and an angle opposite the vertical side labeled "50 degrees". The bamboo pole is represented by the hypotenuse of the triangle.]
Now we can use the trigonometric function tangent to find the length of the bamboo pole.
tan(50 degrees) = opposite/adjacent = h/x
Multiplying both sides by x, we get:
x * tan(50 degrees) = h
Next, we can substitute the values given in the problem:
x * tan(50 degrees) = 15.2 meters
Finally, we can solve for x:
x = 15.2 meters / tan(50 degrees)
Using a calculator, we get:
x ≈ 12.0 meters
Therefore, the length of the bamboo pole is approximately 12.0 meters.