A ladder is leaning against a house and is forming a 60 degree angle with the ground. If the top of the ladder is 18 feet off of the ground, how long is the ladder? Leave your answer in exact form.
sin 60 = opposite/hypotenuse
opposite is 18
solve for hypotenuse
Ha you must be grade 8 cause I got it my text book oh in back it says 4 m
i d k
sin 60 degrees. 18/hyp
x.sin 60=0.8660
18.(0.8660)=x
15.588m = x
To find the length of the ladder, we can use trigonometric functions, specifically the sine function.
The sine function relates the length of the opposite side to the length of the hypotenuse in a right triangle. In this case, the length of the ladder forms the hypotenuse, and the height of the ladder (18 feet) forms the opposite side.
Since the angle formed by the ladder and the ground is 60 degrees, we can use the sine of 60 degrees to find the length of the ladder.
The sine of 60 degrees is √3/2 (approximately 0.866), so we have:
sin(60 degrees) = opposite/hypotenuse
√3/2 = 18/ladder length
Now, we can solve for the length of the ladder:
ladder length = 18 / (√3/2)
ladder length = 18 * (2/√3)
ladder length = (36/√3)
To simplify the answer, we can rationalize the denominator by multiplying both the numerator and denominator by √3:
ladder length = (36/√3) * (√3/√3)
ladder length = (36√3) / 3
ladder length = 12√3
Therefore, the length of the ladder is 12√3 feet in exact form.