Tim has a pool slide that makes an angle of 25 with the water the top of the slide stands 4.5feet above the surface of the water
A:how far out into the pool will the slide reach
B:The slide makes a straight line into the water. How long is the slide
A. 4.5/x = tan 25°
B. 4.5/x = sin 25°
Fdtsf
To find the answer to these questions, we can use trigonometry, specifically the sine function.
A: To determine how far out into the pool the slide will reach, we need to find the length of the slide along the surface of the water. We can use the trigonometric relationship between the angle of elevation and the length of the side opposite the angle.
We know that the angle of elevation is 25 degrees and the height of the top of the slide above the surface of the water is 4.5 feet. Let's call the length we are looking for "x".
Using the sine function, we have sin(25°) = 4.5 / x.
To solve for x, we rearrange the equation as x = 4.5 / sin(25°).
Calculating this, we find x ≈ 10.74 feet. Therefore, the slide will reach approximately 10.74 feet out into the pool.
B: To find the length of the slide, we need to calculate the hypotenuse of the right triangle formed by the slide, the height, and the surface of the water.
We already know the height of the top of the slide above the water surface is 4.5 feet. Let's call the length of the slide "y".
Using the trigonometric relationship between the hypotenuse and the angle of elevation, we have sin(25°) = 4.5 / y.
Rearranging the equation, we have y = 4.5 / sin(25°).
Evaluating this, we find y ≈ 10.74 feet. Therefore, the slide will be approximately 10.74 feet long.