# What is the rate at which the wind blows? Given the following statement: An airplane is travelling due north at an airspeed of 250 km/h when it encounters a wind from the west. The resultant ground velocity is in N20°E. This is a trigonometry question. (recall: SOH CAH TOA)

The ratio for tangent = opposite/adjacent will help us out. Note that the resultant ground velocity is the hypotenuse.

Let w respresent the rate at which the wind blows, so

Tan (20) = w/250

0.364=w/250

w=90.99

Therefore, the wind is blowing from the west at 91 km/h.

Approved by eNotes Editorial Team Let `vecW` be the vector wind. Its magnitude is the wind speed. Its direction is west.

Let  `vecA` be  the airplane velocity.

`vecA+vecW` is the ground velocity written  `vecG` . Its angle is 20 degree.

`vecA` , `vecW` and,  `vecG` determines a right triangle because `vecA _|_ vecW `

In this triangle, the angle `(vecA, vecG)` is 20 degrees.

Therefore `tan 20=W/A`

`W=Atan 20=250tan 20=90.99` km/h

The Wind is 90.99 km/h west

Approved by eNotes Editorial Team