SOLUTION: A ladder is resting against a wall. The ladder and the ground make an angle of 40 degrees and the ladder is 4 ft. from the wall. How long is the ladder?
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Question 656789: A ladder is resting against a wall. The ladder and the ground make an angle of 40 degrees and the ladder is 4 ft. from the wall. How long is the ladder? Found 2 solutions by solver91311, jsmallt9:Answer by solver91311(24713) (Show Source):
You have a right triangle with one of the acute angles measuring 40 degrees. You have the measure of the side adjacent to that 40 degree angle. The cosine of an angle of a right triangle is the measure of the side adjacent divided by the measure of the hypotenuse. The hypotenuse of the triangle is formed by the ladder and therefore the measure of the hypotenuse is the measure of the ladder.
Use your calculator to do the arithmetic.
John
My calculator said it, I believe it, that settles it
You can put this solution on YOUR website! 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.
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.
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):
or
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:
To solve for h we start by multiplying both sides by h:
And then we divide both sides bu 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):
And then divide:
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