Question

A skate board ramp must be set up to rise from the groundat 30°. If the height from the ground to the platform is 8 feet,how far away from the platform must the ramp be set?

Answer 1

To find the distance where the skateboard ramp must be set, we used trigonometry and found the length of the ramp to be 16 feet. Then, using Pythagoras' Theorem, we calculated the base of the right triangle, the horizontal distance, to be approximately 13.86 feet from the platform.

Step-by-step explanation:

The skate ramp problem can be solved using trigonometric principles, particularly with the function of sine, as we are dealing with a right triangle. Using the sine function, where sine of an angle is equal to the opposite side divided by the hypotenuse, we can set up the equation:

sin(30°) = opposite/hypotenuse

sin(30°) = 8 feet / hypotenuse

Since sin(30°) is 0.5, the equation simplifies to:

0.5 = 8 feet / hypotenuse

Now we can solve for the hypotenuse by multiplying both sides by the hypotenuse and then dividing both sides by 0.5:

hypotenuse = 8 feet / 0.5

hypotenuse = 16 feet

The hypotenuse, which is the length of the ramp, is 16 feet. Therefore, the base of the triangle, which is the horizontal distance from the platform where the ramp must be set, can be found using Pythagoras' Theorem:

base² = hypotenuse² - height²

base² = 16² - 8²

base² = 256 - 64

base² = 192

base = √192

base ≈ 13.86 feet

The ramp must be set approximately 13.86 feet away from the platform.

Answer 2

To answer this, first, we have to draw the situation:

height of the ramp is the opposite side, and the distance between the ramp and the platform is the adjacent side (x).

Then, apply the trigonometric function:

Tan 30°= opposite side/ adjacent side

Tan 30° = 8/x

Solve for x:

x= 8/tan 30°

x = 13.85 feet