Bearings Math 11

Question

Alex leaves the dock in his boat on a bearing of 𝑁35°𝐸 and travels 4 km. He then decides to change course to a bearing of 𝑁115°𝐸 and travel for 6 km. How far is Alex from the dock?

Answer 1

SAS triangle , A=180-(115-35)= 100-80=100 degrees

S=4 and 6 km

4-100-6

use cosines law

d^2=4^2+6^2-2(4)(6)Cos100

= 16+36-48Cos100

d=sqr(52-48Cos100)

= 2sqr(13-12Cos100)

= about 6.61 km from the dock