A12-foot ladder rests against a brick wall at angle of 60°. which expression gives the value of x, the height on the brick wall where the ladder rests?

The ladder forms a right triangle whose shorter legs are w and x, the distance of the bottom of the ladder from the wall and the height on the brick wall where the ladder rests:

w^2 + x^2 = (12 ft)^2.

But we are told that the angle between the ladder and the base (w) is 60 degrees.  We want to find x, the height on the wall where the ladder rests.

Thus, sin theta = opp / hyp = x / (12 ft) = sin 60 degrees = (sqrt(3))/2

Solve the equation of ratios  x/ 12 = sqrt(3) / 2.  Cross multiplying, we get 2x = 12 sqrt(3), or x = 6 sqrt(3) (feet)  (answer)

Next time, would you please share the possible answer choices.  Thank you.

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step-by-step explanation:

i hope this : )

the answer to the expression is 83