Question 624353
Draw a right triangle with horizontal and vertical sides. Label the vertical side as 2.65 ft. Label the angle between the horizontal side and the hypotenuse as 6 degrees. We are looking for the length of the ramp, which is the hypotenuse, so label it "x".<br>
To find the length of the ramp we will need to use a Trig function the involves the angle and side we know and the side we want to know. The vertical side is the side opposite to the 6 degree angle and the ramp is the hypotenuse. Which functions have ratios involving opposite and hypotenuse? Answer: sin and csc. Since 6 degrees is not a special angle we will need to use our calculator. And since our calculator probably has a button for sin but not one for csc, we will use sin. Since sin is opposite over hypotenuse the equation we have is:
{{{sin(6) = 2.65/x}}}
Now we solve this for x. We can get rid of the fraction by multiplying both sides by x:
{{{x*sin(6) = 2.65}}}
And then we divide by sin(6):
{{{x = 2.65/sin(6)}}}
This is an exact expression for the answer. For a decimal approximation we reach for our calculators. First we find sin(6):
{{{x = 2.65/sin(6)}}}
{{{x = 2.65/0.10452846}}}
{{{x = 25.35194721}}}
So the ramp will be approximately 25.35 feet long.