A construction company is assembling a slide in a children's playground. The slide is 7.9 m long. If the slide can have a maximum slope of 33°, how high can the top of the slide be?
To determine the maximum height of the slide, we first need to break down the given information.
The length of the slide, L, is 7.9 m, and the maximum slope angle, θ, is 33°.
We can use trigonometric ratios to find the relationship between the length and height of the slide.
In this case, the ratio that relates the opposite side (height) to the adjacent side (length) is the tangent function.
The tangent function is given by: tan(θ) = opposite / adjacent
We can rearrange this equation to solve for the height:
tan(θ) = opposite / adjacent
tan(33°) = height / 7.9 m
Now we can solve for the height:
height = tan(33°) * 7.9 m
height ≈ 0.649 * 7.9 m
Therefore, the top of the slide can be approximately 5.12 m high.
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To determine how high the top of the slide can be, we can use trigonometry. We will use the concept of the right triangle, where the length of the slide is the hypotenuse, and the height we want to find is the opposite side to the angle of 33°.
Let's call the height of the slide "h".
In a right triangle, the trigonometric function that relates the opposite side (h), the hypotenuse (7.9 m), and the angle (33°) is the sine function.
The formula for sine is:
sin(angle) = opposite / hypotenuse
Re-arranging the formula, we have:
opposite = sin(angle) * hypotenuse
Now, we can substitute the known values:
opposite = sin(33°) * 7.9 m
To find the value of sin(33°), we can use a scientific calculator or an online calculator. The sine of 33° is approximately 0.5440.
Substituting this value into our formula, we have:
opposite = 0.5440 * 7.9 m
Solving this calculation, we get:
opposite = 4.4996 m
Therefore, the height of the top of the slide can be approximately 4.4996 meters.