How tall is a building that casts a 78-ft shadow when the angle of elevation of the sun is 31°?

49.91 feet

Step-by-step explanation:

We can solve the exercise by means of the trigonometric ratio of the tangent, since we know the angle between both legs which in this case is the height and length of the shadow, therefore we have to:

tan ° A = opposite / adjacent

° A = 31; adjacent (height) = 78 ft

replacing

tan 34 ° = x / 74

x = tan 34 ° * 74

x = 49.91

that is, the distance from the shadow is 49.91 feet

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.