Two tracking stations are on the equator 158 miles apart. A weather balloon is located on a bearing of N42°E from the western station and on a bearing of N14°W from the eastern station. To the nearest tenth of a mile, how far is the balloon from the western station? *

199.38

Step-by-step explanation:

To better understand the problem I leave an associated graph.

We must calculate the distance of AC, we know AB

AB = 158 miles.

Now we will apply the law of sine where:

AB / sin (° ACB) = AC / sin (° ABC)

We know the ° ABC = 14 °, the statement gives us the ° CAB = 90 ° - 38 ° = 52 °

Now assuming that within a triangle all the angles must add up to 180 °, then

° ACB = 180 ° - 52 ° - 14 ° = 114 °

Solving for AC:

AC = (AB * sin (° ABC)) / sin (° ACB)

AC = (158 * sin (14 °)) / sin (114 °)

AC = 199.38

Therefore the distance between the balloon from the western station is 199.38 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,

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