SOLUTION: A ladder leaning against a house makes an angle of 30 degrees with the ground. the foot of the ladder is 7 feet from the foot of the house. How long is the ladder to the nearest fo

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Question 264217: A ladder leaning against a house makes an angle of 30 degrees with the ground. the foot of the ladder is 7 feet from the foot of the house. How long is the ladder to the nearest foot?
Found 2 solutions by mananth, dabanfield:
Answer by mananth(16946) About Me  (Show Source):
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A ladder leaning against a house makes an angle of 30 degrees with the ground. the foot of the ladder is 7 feet from the foot of the house. How long is the ladder to the nearest foot?
Cos 30 = base / hypotenuse
0.154= 7/hypotenuse
7/0.154
=45.45



Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
A ladder leaning against a house makes an angle of 30 degrees with the ground. the foot of the ladder is 7 feet from the foot of the house. How long is the ladder to the nearest foot?
Let L be the length of the ladder. The ladder and the side of the house form a right triangle with the ladder being the hypotenuse and the house wall being the side opposite the 30 degree angle. We have a theorem that says that in a right triangle the side opposite a 30 degree angle is half the hypotenuse, in this case L/2.
So by Pythagorean Theorem we have:
L^2 = (L/2)^2 + 7^2 or
L^2 = (L^2)/4 + 49
Solve the above for L.