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Sphinxa [80]
3 years ago
14

In the San Gabriel Mountains in California, lookout station Running Deer is 18 kilometers due west of station Lazy Bear. The bea

ring from Running Deer to a fire directly south of Lazy Bear is S38.4°E. To the nearest tenth of a kilometer, how far is the fire from Running Deer?

Mathematics
1 answer:
Lera25 [3.4K]3 years ago
4 0

Answer:

29.0 kilometers

Step-by-step explanation:

From the figure attached,

Lookout station Running Deer is at A, Station Lazy Bear is at B and Fire is at C.

Bearing from Running deer to Fire is S38.4°E.

Therefore, m∠SAC = m∠ACB = 38.4°

Distance between the stations Running Deer and Lazy Beer = 18 km

From the given triangle ABC,

Sin(C) = \frac{\text{Opposite side}}{\text{Hypotenuse}} = \frac{\text{AB}}{\text{AC}}

Sin(38.4)° = \frac{18}{y}

y = \frac{18}{\text{Sin}38.4}

y = 28.978 ≈ 29.0 km

Therefore, distance between Fire and Running deer is 29 kilometers.    

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The shape consists of a rectangle on the bottom and a trapezoid on the top.

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Trapezoid

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