Question

In extremely large​ forests, it is not​ cost-effective to position forest rangers in towers or to use small aircraft to continually watch for fires. Since lightning is a frequent cause of​ fire, lightning detectors are now commonly used instead. These devices not only give a bearing on the location but also measure the intensity of the lightning. A detector at point Q is situated 11 miles west of a central fire station at point R. The bearing from Q to where lightning hits due south of R is S37.3​°E. How far is the hit from point​ R?

Answer 1

Answer:

Point R is at 14.28 miles.

Explanation:

According to the attached image:

Q = 90 - 37.6 = 52.4°

Using the tangent property:

tanθ = s/11

s = 11 * tanθ = 11 * tan52.4 = 14.28 miles