Question

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

Answer 1

29.0 kilometers

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)° =
`(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.