in a park some people are launching model rockets to find the maximum height,x,the rocket reaches, a person stands 50.0m from the launch sight and measure the angle from the ground to the rocket at its maximum height. if the angle is 36 then the maximum height,x, of rocket is----m
Did you make a diagram?
Looks like a right-angled triangle to me, where the angle is 36ΒΊ, the adjacent is 50 and the opposite is h.
tan 36 = h/50
solve for h
To find the maximum height, x, of the rocket, we can use trigonometry. Specifically, we will use the tangent function, which relates the angle of elevation to the respective side lengths.
Here's how we can solve the problem step-by-step:
1. Draw a diagram: Draw a right triangle representing the situation. Label one side as 50.0 m (the distance from the person to the launch site) and another side as x m (the maximum height of the rocket). The angle of elevation, 36 degrees, should be opposite the side representing the maximum height.
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x | \
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50
2. Use the tangent function: The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is x m and the adjacent side is 50.0 m. So we can write:
tan(36) = x / 50.0
3. Solve for x: Now, we can rearrange the equation to solve for x. Multiply both sides of the equation by 50.0:
x = 50.0 * tan(36)
4. Calculate the result: Use a calculator to find the tangent of 36 degrees, then multiply it by 50.0 to get the maximum height, x, of the rocket.
x β 50.0 * 0.7265 β 36.325 m
Therefore, the maximum height, x, of the rocket is approximately 36.325 meters.