Domenic and Adriana are observing a hot-air balloon from two tracking stations on the ground. The tracking stations are 6.0 km apart. From Domenic's point of view, the hot-air balloon is at an
angle of elevation of 72º. From Adriana's point of view, the angle of elevation is 58º.

height of the balloon = 6.32 km

Step-by-step 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

expression #3 is not equivalent. the others are.

answer is 12345678900987654321234567890987654321

step-by-step explanation: