<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B8%7Dx%20%20%2B%2013%20%3D%2018" id="TexFormula1" title=" \frac{5}{8}x + 1

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Keith_Richards [23]

4 years ago

12

3 = 18" alt=" \frac{5}{8}x + 13 = 18" align="absmiddle" class="latex-formula">

1 answer:

zhenek [66]4 years ago

8 0

$\frac{5}{8}x + 13 = 18 \\ \frac{5}{8} x = 18 - 13 \\ \frac{5}{8} x = 5 \\ 5x = 40 \\ x = 8$

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NGC is a hot air balloon in the sky from her spot on the ground. The angle of elevation from Angie to the balloon is 40°. If she

Goshia [24]

Answer:

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Step-by-step explanation:

Labelled diagram of given scenario is shown below.

Given that,

An angle of elevation of Hot air balloon by Angie is $40$ °.

When she stepped back $200 ft$ then angle of elevation was $10$ °.

Height of Angie is $5.5 ft$ .

To find: How far off the ground is a hot air balloon.

So, from figure

Height of Angie $(BC) = 5.5ft$

In triangle Δ $ABD$ ,

⇒ $tan {40\si {\degree}} = \frac{AB}{BD}$

⇒ $AB = tan (40) \times BD$ ....................(1)

Now, In triangle Δ $ABE$

⇒ $tan (10)= \frac{AB}{200+BD}$

⇒ $AB = tan(10)\times (200+BD)$

Here, substituting the value $AB$ from Equation (1) we get,

$tan(10)\times (200+BD)= tan(40)\times BD$

$tan(10)\times 200+tan(10)\times BD= tan(40)\times BD$

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Therefore Length of $AC= AB+BC$ = $(44.6457 + 5.5) ft$

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Hence,

The distance from hot air balloon to the ground $AC=50.1457 ft$ .

6 0

3 years ago