A man standing near a radio station antenna observes that the angle of elevation to the top of the antenna is A = 67°. (Rest of question is in description box)

Question

He then walks s = 100 feet further away and observes that the angle of elevation to the top of the antenna is B = 45° . Find the height of the antenna to the nearest foot. (Hint: Find x first.)

Answer 1

s = hcot45° - hcot67°; h = s/(1 - cot67°); h = 100/(1 - cot67°) = 174 feet

Answer 2

Draw and label a diagram

h represents the height of the tower

d represents the distance from the tower to first observation point

h / d = tan 67°

h = d tan 67°

h / tan 67° = d (eq 1)

h / (d + 100) = tan 67°

h = (d + 100) tan 67°

h / tan 67° = d + 100

(h / tan 67°) - 100 = d (eq 2)

Set eq1 equal to eq 2 and solve for h.