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Take the tangent of angle a, its gives us tan a = 4/5. ( Tangent = opposite/ adjacent). So 4/5 = 0.8. To find the angle a we take the inverse tangent of 0.8 which gives us
A ladder is resting against a wall. The ladder and the ground make an angle of 45° and the ladder is 7 ft from the wall. How long is the ladder?
Let the length of the ladder be x, to find x we use the cosine of 45, so its cos 45= 7/x, solving for x in that equation we get x=7/cos 45, x becomes 9.8 feet.
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so here you are given the following values:
Angle = 45 degrees
adjacent length = 7ft
so we use the cosine rule:
cos(angle) = adjacent/hypotenuse
rearrange to fit our question (we are trying to find the hypotenuse, length of ladder)
hypotenuse = adjacent/cos(angle)
Length = 7/cos(45)
therefore the ladder is 9.9ft long
Actually, Isaiah.Feynman, 9.8ft is not correct and would result in the deduction of marks on an exam.
Correctly rounded, the answer is 9.9ft.
@Omistone I didn't round at all, but thanks for the heads up.