Answer:
height of the balloon = 6.32 km
Explanation:
The question wants us to find the height of the balloon .
They are observing the balloon from two tracking stations on the ground. The tracking stations are 6 km apart . From Dominic point of view the hair balloon is at an angle of elevation of 72° and from Adriana point of view the elevation is 58° . The illustration forms a triangle containing 2 right angles with a similar height.
To find the height we must find the hypotenuse of one of the right angle triangle. WE are given 2 angle and a side of 6 km. The third angle is 180 - 72 - 58 = 50°.
Using sin rule
6/sin 50° = b/sin 72°
cross multiply
6 sin 72° = b sin 50°
divide both sides by sin 50°
b = 6 sin 72°/sin 50°
b = 6 × 0.95105651629 /0.76604444311
b = 5.70633909777 /0.76604444311
b = 7.44909665372
b ≈ 7.45 km
The height can be found since we know the hypotenuse of one side of one of the right angle triangle.
sin 58° = opposite/hypotenuse
sin 58° = h/7.45
cross multiply
h = 7.45 × sin 58°
h = 7.45 × 0.84804809615
h = 6.31795831637
h ≈ 6.32 km