Question

An airplane is flying from city A to city B at a bearing of 100 degrees. The distance between the two cities is 1200 miles. How far west is city A relative to city B ? Round your answer to the nearest mile.

Answer 1

`\displaystyle 1182\:mi.`

Step-by-step explanation:

`\displaystyle (OPPOCITE)/(HYPOTENUSE) = sin\:\theta \\ (ADJACENT)/(HYPOTENUSE) = cos\:\theta \\ (OPPOCITE)/(ADJACENT) = tan\:\theta \\ (HYPOTENUSE)/(ADJACENT) = sec\:\theta \\ (HYPOTENUSE)/(OPPOCITE) = csc\:\theta \\ (ADJACENT)/(OPPOCITE) = cot\:\theta`

You are travelling from one location to another at a directional angle of 100°. So, we will use the cosecant trigonometric ratio to determine how far west the aeroplane travelled to its destination:

`\displaystyle (1200)/(w) = csc\:100 \\ (1200)/(csc\:100) = w \\ \\ 1181,7693036... = w \\ \\ \boxed{1182 \approx w}`

I am joyous to assist you at any time.

Answer 2

Explanation:

`sin~100=(h)/(1200)\\h=1200*sin*100 \approx 1181.7\\\approx ~1182~mile`