Question
5ft/sin(4.8)? what is are ramp length
Answers
GPT-4o mini
To find the ramp length using the formula you provided, it seems you're considering a right triangle where \(5\) ft is the height and the angle is \(4.8\) degrees.
In a right triangle, the sine of an angle is given by:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
where:
- "opposite" is the height of the triangle (5 ft),
- "hypotenuse" is the length of the ramp you want to find,
- \(\theta\) is the angle (4.8 degrees).
We can rearrange this formula to find the hypotenuse (ramp length):
\[
\text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)}
\]
Substituting in the given values:
\[
\text{hypotenuse} = \frac{5}{\sin(4.8^\circ)}
\]
Now, we can compute \(\sin(4.8^\circ)\):
Using a calculator or sine table:
\(\sin(4.8^\circ) \approx 0.0834\)
Now substituting this value:
\[
\text{hypotenuse} \approx \frac{5}{0.0834} \approx 60.024
\]
So the ramp length is approximately **60.02 feet**.
In a right triangle, the sine of an angle is given by:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
where:
- "opposite" is the height of the triangle (5 ft),
- "hypotenuse" is the length of the ramp you want to find,
- \(\theta\) is the angle (4.8 degrees).
We can rearrange this formula to find the hypotenuse (ramp length):
\[
\text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)}
\]
Substituting in the given values:
\[
\text{hypotenuse} = \frac{5}{\sin(4.8^\circ)}
\]
Now, we can compute \(\sin(4.8^\circ)\):
Using a calculator or sine table:
\(\sin(4.8^\circ) \approx 0.0834\)
Now substituting this value:
\[
\text{hypotenuse} \approx \frac{5}{0.0834} \approx 60.024
\]
So the ramp length is approximately **60.02 feet**.