Question

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?

Answer 1

Answer:

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

$tan \theta = \frac{Perpendicular}{Base}$

$tan 45^{\circ} = \frac{AD}{BD}$

$1= \frac{h}{x}$

$x=h$ ---1

In ΔACD

Using trigonometric ratio

$tan \theta = \frac{Perpendicular}{Base}$

$tan 60^{\circ} = \frac{AD}{DC}$

$\sqrt{3}= \frac{h}{100-x}$

$\sqrt{3}(100-x)=h$ ---2

So, equating 1 and 2

$\sqrt{3}(100-x)=x$

$100\sqrt{3}-\sqrt{3}x=x$

$100\sqrt{3}=x+\sqrt{3}x$

$100\sqrt{3}=x(1+\sqrt{3})$

$\frac{100\sqrt{3}}{1+\sqrt{3}}=x$

$63.39=x$

Thus the height of the balloon is 63.39 yards.

Answer 2

Answer:

B

Step-by-step explanation: