Question
A 25-foot ladder stands against a vertical wall at an angle of n degrees with the ground. If sin n = 4 / 5, how far is the base of the ladder from the wall?
A. 12
B. 13
C. 14
D. 15
E. 16
A. 12
B. 13
C. 14
D. 15
E. 16
Answers
Neil
Sin n = 4 / 5. Remember that the formula for sin would be Opposite / Hypotenuse. So:
Sin n = Opposite / Hypotenuse = 4 / 5
Sine n = Opposite / 25 = 4 / 5
5 Opposite = 100
5 / 5 Opposite = 100 / 5
Opposite = 20.
Now what we do is use Pythagorean Theorem to find the length of the adjacent side.
a^2 + b^2 = c^2
20^2 + b^2 = 25^2
400 + b^2 = 625
400 - 400 + b^2 = 625 - 400
b^2 = 225
sqrt(b^2) = sqrt(225)
b = 15.
Answer choice D
Sin n = Opposite / Hypotenuse = 4 / 5
Sine n = Opposite / 25 = 4 / 5
5 Opposite = 100
5 / 5 Opposite = 100 / 5
Opposite = 20.
Now what we do is use Pythagorean Theorem to find the length of the adjacent side.
a^2 + b^2 = c^2
20^2 + b^2 = 25^2
400 + b^2 = 625
400 - 400 + b^2 = 625 - 400
b^2 = 225
sqrt(b^2) = sqrt(225)
b = 15.
Answer choice D