How tall is a building that casts a 66-ft shadow when the angle of elevation of the sun is 29°?

36.58° ft

Step-by-step explanation

To solve this, you need to consider the complete visual as a triangle.

(Refer to the attached picture for better understanding)

We are assuming that the building  stands at an angle of 90° to the ground, making the triangle a right-angled triangle. We can apply the trignometric formula that links an angle to two sides: perpendicular, which is the height of the building (a) in this case, and base, the length of the shadow cast (b) by the building of known length.

tan(θ) = length of perpendicular (a) / length of base (b)

We are using this formula, as we know the values of the above mentioned sides of the triangle.

Solve:

tan(29°) = P / 66

0.554 x 66 = P

36.58 = P

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b