91Ó°ÊÓ

In attempting to fly from Chicago to Louisville, a distance of a $330$miles, a pilot inadvertently took a course that was $10°$in error.

If the aircraft maintains an average speed of $220$miles per hour and if the error in direction is discovered after $15$minutes, the distance covered is $220×0.25=55$miles . Let -

Now,$a^2=b^2+c^2-2bc\cos A$

role="math" localid="1646934010066" $={330}^2+{55}^2-2×330×55\cos 10°$

role="math" localid="1646934326858" $a≈276$

We have to find angle C -

$\frac{\sin A}{a}=\frac{\sin C}{c}$

role="math" localid="1646934412665" $\frac{\sin 10°}{276}=\frac{\sin C}{55}$

${\sin }^{-1}\frac{55\sin 10°}{276}=C$

role="math" localid="1646934617058" $2°≈C$

We know, $10°+B+2°=180°$

$B≈168°$

The angle the pilot should turn to head toward Louisville is -

$180°-168°≈12°$

In attempting to fly from Chicago to Louisville, a distance of a $330$miles, a pilot inadvertently took a course that was $10°$in error.

Here the distance after turning to head toward Louisville is $276$miles and the total time of the the trip is $90$minutes or $1.5$hours. So, the new average speed the pilot should maintain is -

$\frac{276}{1.5}≈184$ miles per hour