Hang glider height: ~1999 ft (adding heights from both observers)
Triangle ABC: Missing angle C ≈ 80°, side BC ≈ 9.1 ft (using Law of Sines)
Part 1: Finding the height of the hang glider
Solution:
Identify relevant triangles: We have two right triangles: triangle ABC (with observers A and B at the base and the hang glider at the top) and triangle ABD (with observer A at the base, observer B at the midpoint, and the hang glider at the top).
Angles and distances: We are given the angles of elevation (61° for AB and 49° for BD) and the distance between the observers (AB = 1663 ft).
Use trigonometry:
For triangle ABC (right at observer B): sin(61°) = h / AB --> h = AB * sin(61°) = 1663 ft * sin(61°) ≈ 1482 ft (height of hang glider above B)
For triangle ABD (right at observer A): sin(49°) = h / (AB/2) --> h = (AB/2) * sin(49°) = (1663 ft / 2) * sin(49°) ≈ 517 ft (height of hang glider above A)
Find the actual height: The actual height of the hang glider is the sum of the height above each observer: h_total = h_above_B + h_above_A ≈ 1482 ft + 517 ft ≈ 1999 ft
Therefore, the height of the hang glider is approximately 1999 feet.
Part 2: Finding the remaining angle and sides in triangle ABC
Solution:
Given information: A = 65°, B = 35°, a = 15 ft (side AB)
Law of Sines: Since we have an angle and a side opposite to it in triangle ABC, we can use the Law of Sines to find the remaining sides and missing angle.
Side BC: sin(A) / a = sin(B) / BC --> BC = a * sin(B) / sin(A) ≈ 15 ft * sin(35°) / sin(65°) ≈ 9.1 ft
Missing angle C: C = 180° - A - B = 180° - 65° - 35° = 80°
Therefore, in triangle ABC, angle C is approximately 80° and side BC is approximately 9.1 feet.
The probable question is in the image attached.