Question

Rajani wants to use a sheet of fiberboard 31 inches long to create a skateboard ramp

with a 19° angle of elevation from the ground. How high will the ramp rise from the
ground at its highest end? Round your answer to the nearest tenth of an inch if
necessary.

Answer 1

To find the height of a skateboard ramp with an angle of elevation of 19° and a length of 31 inches, use the sine function: height = sine(angle) x length of the ramp, calculate sine(19°), and multiply by 31, rounding to the nearest tenth.

Step-by-step explanation:

The student is asking about how to determine the height at the highest end of a skateboard ramp given the length of the ramp and the angle of elevation. This is a trigonometry problem where the height of the ramp can be found using the sine function. The sine of an angle in a right triangle is equal to the opposite side (height) divided by the hypotenuse (length of the ramp).

To find the height (h) at the highest end of the ramp, the formula used is:

1. h = sine(angle) × length of the ramp
2. h = sine(19°) × 31 inches
3. Calculate the sine of 19° using a calculator.
4. Multiply this value by 31 to get the height.
5. Round your result to the nearest tenth of an inch if necessary.

Therefore, by following this procedure, Rajani can find out how high her skateboard ramp will rise from the ground at its highest end.

Answer 2

Answer: 10.1

Step-by-step explanation: sin 19=

hypotenuse

opposite

​

=

31

x

​

sin

19

=

sin 19=

 

 

�

31

31

x

​

sin

19

1

=

1

sin 19

​

=

 

 

�

31

31

x

​

31

sin

19

=

31 sin 19=

 

 

�

x

Cross multiply.

�

=

10.092612...

≈

10.1

x=10.092612...≈10.1

Type into calculator and round to the nearest tenth.

The ramp will rise 10.1 inches from the ground.

The ramp will rise 10.1 inches from the ground.