Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from B, a distance of about 456.2456.2 miles. A second flight option flies first to city C and then connects to A. The bearing from B to C is N2929degrees°E, and the bearing from B to A is N59.759.7degrees°E. The bearing from A to B is S59.759.7degrees°W, and the bearing from A to C is N78.978.9degrees°W. How many more frequent flyer miles will Adam receive if he takes the connecting flight rather than the direct flight? Adam would receive nothing more frequent flyer miles.

105.6 miles

Step-by-step explanation:

In the diagram

The angle at B = 59.7°-29°=30.7°

The angle at A =180°-(78.9°+59.7°)=41.4°

Using the sum of angles in a triangle, Angle C = 107.9°

Applying the Law of Sines

Similarly

Therefore:

AC+BC=244.76+317.04 =561.8 miles

Difference

561.8 - 456.2 =105.6 miles

Therefore, Adam would receive 105.6 miles more frequent flyer miles.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,