Trigonometry Bearing Question

Question

A sailing boat sails south for 117 km, then on a bearing of 051° until it is due east of its starting point. How far is the boat from its starting point?

Answer 1

For your set-up side "a"=117; angle "β"=51°; "α"=39°; "γ" is the rt angle.

A set of formulas is: a/(sinα)=b/(sinβ)=c; the sin of a rt angle (γ)=1.

Given: 117/(sin39)=185.91="c".

Now you want side "b". Another formula is a^2+b^2=c^2; so: 185.91^2-117^2=20875^.5=144.482......km.

Answer 2

Bearings are measured clockwise from the reference of north = 0^o

OA is 117km

∠OAE is 51^o

OE is what we seek to find

tan(∠OAE) = opposite / adjacent = OE / OA

tan(51^o) = OE / 117km

Multiply both sides by 117km, to get:

OE = tan(51^o)*117km

OE = 144.48km

(Figure is not to scale)

O E

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A