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Brut [27]
2 years ago
14

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 a

t a 60° angle to see the same hot air balloon. Approximately how far is the hot air balloon off the ground?

Mathematics
2 answers:
vlabodo [156]2 years ago
7 0

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.

Paha777 [63]2 years ago
5 0

Answer:

B

Step-by-step explanation:

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