Caleb and emily are standing 100 yards from each other. caleb looks up at a 45° angle to see a hot air balloon. emily looks up at a 60° angle to see the same hot air balloon. approximately how far is the hot air balloon off the ground?

63.39 yards.

Step-by-step explanation:

Refer the attached figure

We are given that Caleb and Emily are standing 100 yards from each other i.e. BC = 100

Let BD = x

So, DC = 100-x

We are given that Caleb looks up at a 45° angle to see a hot air balloon i.e. ∠ABD = 45° and  Emily looks up at a 60° angle to see the same hot air balloon i.e. ∠ACD = 60°

Let AD be the height of the balloon denoted by h.

In ΔABD

Using trigonometric ratio

---1

In ΔACD

Using trigonometric ratio

---2

So, equating 1 and 2

Thus the height of the balloon is 63.39 yards.

step-by-step explanation: