Answer to Question #92109 in Trigonometry for Toshinori

Question

After taking off from the landing pad, a helicopter flies 9 miles south, then 8 miles northeast. How far is the helicopter from the landing pad (s), and in what direction (pheta) must it fly to head directly back to the landing pad?

s= and
pheta = (0 degree <= pheta < 360 where East is 0 degree and North is 90 degree).

Answer 1

Using the cosine rule,

x²=8²+9²-2*8*9cos 45⁰

x²=69.35

x=8.328 miles from s

9/sin y=8.328/sin45⁰

sin y=9sin45⁰/8.328=0.9196

y=arcsin 0.9196=66.87⁰.

To get back to s it travels in the direction 180⁰+(66.87⁰-45⁰)=201.87⁰.