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:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.