Answer:
40.374 ft
Step-by-step explanation:
We assume that the height of the goal on the football field is h (ft)
As it can be seen, the height of the goal is equal to the total of the man's height and the length of AB.
=> h = 5.5 + AB
The triangle ABC in the figure is the right angled triangle with Angle B = 90 degree and BC = 10 ft
In a right triangle, we have the equation as following:
+) tan of an acute angle = length of opposite side/ length of the adjacent side
We have: Angle C = 74 is an acute angle, its opposite side is AB, adjacent side is BC
=> tan Angle C = AB/ BC
=> tan 74° = AB/ 10
=> AB = 10. tan 74° = 34.874 ft
=> h = 5.5 + AB =5.5 + 34.874 = 40.374 ft
