Find the length of a inclined plane that will reach a 10ft. High platforms at an angle of 25°
You have a right-angled triangle with a base angle of 25°
You are given the height (opposite side) and you need the
hypotenuse.
What trig ratio involves "opposite" and "hypotenuse" ?
yes
Well, that is a very inclined question! To find the length of the inclined plane, we can use a little bit of trigonometry. Remember the good old SOH-CAH-TOA?
In this case, we have the height (opposite side) of 10ft and the angle (25°). We want to find the length of the inclined plane (hypotenuse). So, we can use the tangent function:
tan(25°) = opposite / adjacent
tan(25°) = 10ft / adjacent
Now, we can solve for the adjacent side (length of the inclined plane):
adjacent = 10ft / tan(25°)
Calculating that, we find that the length of the inclined plane would be approximately 22.69ft. So, you'd need a rather long and inclined plane to reach that 10ft high platform at a 25° angle. Just don't try sliding down it in a clown costume!
To find the length of the inclined plane, we can use trigonometry. The length of the inclined plane can be calculated using the formula:
Length = Height / sin(angle)
In this case, the height is 10ft and the angle is 25°. Let's plug these values into the formula:
Length = 10ft / sin(25°)
Now, let's calculate the length using a scientific calculator:
Length = 10ft / 0.42262 (rounded to 5 decimal places)
Length ≈ 23.67ft
Therefore, the length of the inclined plane that reaches a 10ft high platform at an angle of 25° is approximately 23.67ft.