A playground slide starts 107cm above the ground and is 250cm long. What angle does the slide make with the ground? Give the answer to the nearest degree.

"A playground slide starts 107cm above the ground and is 250cm long"

Trusting my English grammar somewhat, you made "slide" the subject of your sentence, and you said it is 250 cm long.
Thus 250 is the hypotenuse.
tanØ = opposite/adjacent
sinØ = opposite/hypotenuse
cosØ = adjacent/ hypotenuse

according to your data, the angle is 25° to the nearest degree

well, if you insist on using tan, then note that the base of the slide is

√(250^2 - 107^2) = 225.9 cm out from spot directly under the slide's top.

So, now we have

tan θ = 107/225.9 = 0.47
θ = 25.3°

But this section is on tan only and the answer is 24.

Well, if you're looking for the "angle of slide" information, I'm guessing you're not just interested in the slide's ability to make children scream in delight. Let's calculate it then!

To find the angle, we can use trigonometry. The slide's height (opposite side) is 107 cm, and the slide's length (hypotenuse) is 250 cm. So, we can use the tangent function (tan(angle) = opposite/adjacent).

tan(angle) = 107 cm / 250 cm
angle = tan^(-1)(107/250)

Now, let me consult my joke calculator, ahem, I mean, do some quick math here.

Calculating, calculating...

And the answer is approximately 23 degrees to the nearest degree! So, you better slide down that slope with a big smile... and maybe bring a banana peel for extra fun.

To find the angle that the slide makes with the ground, we can use trigonometry. The angle we need to find is the angle between the slide and the horizontal ground.

1. Draw a right triangle with the slide as the hypotenuse, the height as the opposite side, and the length of the slide as the adjacent side.
- The height of the slide is given as 107 cm, and the length of the slide is given as 250 cm.

2. Now, we need to find the angle between the horizontal ground and the slide. We can use the trigonometric function called tangent (tan).

3. The tangent of the angle is defined as the ratio of the length of the opposite side (height) to the length of the adjacent side (slide length). We can write this as follows:
- tan(angle) = height / slide length

4. Substitute the given values into the equation:
- tan(angle) = 107 cm / 250 cm

5. Calculate the tangent of the angle:
- tan(angle) ≈ 0.428

6. To find the angle, we can take the inverse tangent (arctan) of both sides:
- angle ≈ arctan(0.428)

7. Using a calculator or an online tool, calculate the arctan of 0.428:
- angle ≈ 23.4 degrees (rounded to the nearest degree).

Therefore, the angle that the slide makes with the ground is approximately 23 degrees.

Assuming the slide is a straight line, (most are not)

Did you make your sketch?
I have the opposite as 107 and the hypotenuse as 250

so sinØ = 107/250
Ø = appr 25°