Answer: The height of the goalpost is 41.6 feet (to the nearest tenth of a foot)
Step-by-step explanation: The figure shows an observer looking up at a goalpost at an angle of elevation of 61 degrees. The observer is 20 feet away from the base of the goalpost and he is standing 5.5 feet from the ground. This means the total height of the goalpost shall be an addition of the observer's height plus the calculated length of the portion of the goalpost as indicated by the right angled triangle.
We now have a right angled triangle, with one of the other two angles measuring 61 degrees and this shall be the reference angle. The side facing the reference angle is the opposite and is yet unknown. Also, the length from his position to the base of the goalpost is the adjacent (the side that lies between the right angle and one of the other two sides. To calculate the height,
Tan 61 = opposite/adjacent
Tan 61 = opposite/20
Tan 61 x 20 = opposite
1.8041 x 20 = opposite
36.082 = opposite.
Remember that the entire length of the goalpost includes the height of the observer (which is 5.5 ft). The height of the goalpost therefore is
Height = 5.5 + 36.082
Height = 41.582
The height of the goalpost rounded to the nearest tenth of a foot is
41.6 feet
