a slide 5.4 meters long makes an angle of 29 degrees with the ground. How far above is the top of the slide?
Is this geometry or trigonometry?
If the top is at height h,
h/5.4 = sin 29°
h = 5.4 * sin 29°
h = 5.4 * 0.4848
h = 2.6 meters
This makes sense, since sin 30° = 1/2, which would make the slide half as high as it is long.
To find out how far above the ground the top of the slide is, we can use trigonometry. Here's how you can solve it step by step:
Step 1: Identify the trigonometric function to use.
Since we are given an angle and the opposite side length, the trigonometric function that relates these two information is the sine function (sin).
Step 2: Set up the equation using the sine function.
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the height of the slide, and the hypotenuse is the length of the slide. The angle is given as 29 degrees.
So, we have: sin(29 degrees) = height/5.4 meters
Step 3: Solve for the height.
To isolate the height, we can rearrange the equation:
height = sin(29 degrees) * 5.4 meters
Step 4: Calculate the answer.
Using a calculator, evaluate sin(29 degrees) to get its numerical value and then multiply it by 5.4 meters.
By following these steps, you can calculate the height of the top of the slide above the ground.