A slide 2.6 m long makes an angle of 27° with the ground. How high is the top of the slide above the ground?
Could someone show me how to solve this? I'm not sure where to begin.
sin 27 = h/2.6
so
h = 2.6 sin 27
Thank you so much for your help!
To solve this problem, we can use trigonometry. The given information is the length of the slide (2.6 m) and the angle it makes with the ground (27°).
First, we need to identify which trigonometric function to use. Since we are given the length of the slide and want to find the height, we can use the sine function, which relates the opposite side (height) to the hypotenuse (slide length).
The formula for sine is:
sin(angle) = opposite / hypotenuse
In this case, the angle is 27°, the opposite side is the height we want to find, and the hypotenuse is the length of the slide (2.6 m).
So, the equation becomes:
sin(27°) = height / 2.6 m
To solve for the height, we can rearrange the equation and isolate the height:
height = sin(27°) * 2.6 m
Using a calculator, we can find the sine of 27°, which is approximately equal to 0.454.
height = 0.454 * 2.6 m
Finally, we can calculate the height:
height ≈ 1.177 m
Therefore, the top of the slide is approximately 1.177 meters above the ground.
To solve this problem, you can use trigonometry, specifically the sine function. Here's how you can solve it step-by-step:
1. Draw a diagram of the problem to visualize it better. Draw a right triangle, where the bottom side represents the ground, the slide represents the hypotenuse, and the height represents the vertical distance to be found.
2. Identify the angle. In this case, the angle is given as 27°.
3. Recall that the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we want to find the length of the side opposite the angle, which is the height.
4. Substitute the given values into the sine formula:
sin(angle) = opposite / hypotenuse
In this case, angle = 27° and hypotenuse = 2.6 m.
sin(27°) = height / 2.6 m
5. Solve for the height.
Multiply both sides of the equation by 2.6 m:
2.6 m * sin(27°) = height
Use a calculator to find the sine of 27°:
sin(27°) ≈ 0.454
Substitute the value:
2.6 m * 0.454 ≈ height
Calculate:
height ≈ 1.1816 m
Therefore, the top of the slide is approximately 1.1816 meters above the ground.