Question

PLEASE PLEASE HELP!! Sketch a triangle and label correctly. Work must be shown for this problem. Round answers to the nearest hundredth (2 decimal places).

Answer 1

Please see attached image for the sketch with the labels.

Length "x" of the ramp = 11.70 ft

Explanation:

Notice that the geometry to represent the ramp is a right angle triangle, for which we know one of its acute angles (
`20^o`), and the size of the side opposite to it (4 ft). Our unknown is the hypotenuse "x" of this right angle triangle, which is the actual ramp length we need to find.

For this, we use the the "sin" function of an angle in the triangle, which is defined as the quotient between the side opposite to the angle, divided by the hypotenuse, and then solve for the unknown "x" in the equation:

`sin(20^o)=(opposite)/(hypotenuse)\\ sin(20^o)=(4)/(x) \\x=(4)/(sin(20^o)) \\x=11.695\,\,ft`

Therefore the length of the ramp rounded to the nearest hundredth as requested is: 11.70 ft