# How Long is the New Ramp?

• Nov 14th 2008, 01:11 PM
magentarita
How Long is the New Ramp?
A loading ramp 10 feet long that makes an angle of 18 degrees with the horizontal is to be replaced by one that makes an angle of 12 degrees with the horizontal. How long is the new ramp?

• Nov 14th 2008, 01:38 PM
masters
Quote:

Originally Posted by magentarita
A loading ramp 10 feet long that makes an angle of 18 degrees with the horizontal is to be replaced by one that makes an angle of 12 degrees with the horizontal. How long is the new ramp?

The second loading ramp will have to reach the same height as the first one. We just need to know what that height is.

$\sin 18^{\circ}=\frac{h}{10}$

$h=10\sin 18^{\circ}$

Without rounding we can get a more accurate measure. So, I'll use the expression in the next calculation instead of an approximation.

$\sin 12^{\circ}=\frac{10\sin 18^{\circ}}{x}$

$x\sin12^{\circ}=10\sin 18^{\circ}$

$x=\frac{10\sin 18^{\circ}}{\sin 12^{\circ}}\approx 14.86$ ft.
• Nov 14th 2008, 05:14 PM
magentarita
great..........
Quote:

Originally Posted by masters
The second loading ramp will have to reach the same height as the first one. We just need to know what that height is.

$\sin 18^{\circ}=\frac{h}{10}$

$h=10\sin 18^{\circ}$

Without rounding we can get a more accurate measure. So, I'll use the expression in the next calculation instead of an approximation.

$\sin 12^{\circ}=\frac{10\sin 18^{\circ}}{x}$

$x\sin12^{\circ}=10\sin 18^{\circ}$

$x=\frac{10\sin 18^{\circ}}{\sin 12^{\circ}}\approx 14.86$ ft.

Great notes like always.