Question 656789
This might be easier if you draw a diagram. Draw a right triangle with legs that are vertical and horizontal. The vertical side is the wall, the horizontal side is the ground and the hypotenuse is the ladder. Label the ground side as 4 and the angle between the ground and the ladder as 40 degrees.<br>
Since we are looking to find the length of the ladder, we are looking for the length of the hypotenuse in our drawing. In our triangle we know one side and an angle and we are looking for the hypotenuse.<br>
The side we know and the side we want are, in relation to the angle we know, the adjacent side and the hypotenuse. There are two Trig ratios/functions that involve the adjacent side and the hypotenuse: cos and sec. So we can use either of the following equations to find the hypotenuse (using "h" for the hypotenuse):
{{{cos(40) = 4/h}}}
or
{{{sec(40) = h/4}}}<br>
Since 40 degrees is not a special angle we will need to use our calculators on this problem. And since our calculators do not have a sec button, we will use the cos equation:
{{{cos(40) = 4/h}}}
To solve for h we start by multiplying both sides by h:
{{{h*cos(40) = 4}}}
And then we divide both sides bu cos(40):
{{{h = 4/cos(40)}}}
This is an exact expression for the length of the ladder. But you probably want a decimal approximation. So we got to our calculators to find cos(40):
{{{h = 4/0.76604444}}}
And then divide:
{{{h = 5.22162916}}}<br>
So the ladder is approximately 5.2 feet long.