How far did the skater skate from point A to B?

Question

A skater ⛸️ skated along a straight path from point A to point B . Consider the following:

Two streets that intersect at point C also intersect the path at points A and B .

Street AC = 0.6 mi and street BC = 1.2 mi .

The included angle at C = 107° .

How far did the skater skate from point A to B ?

Thank you friends.

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Answer 1 · 2017-11-27T22:44:55

See below.

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Not absolutely clear on the question, could have done with a sketch.

From the known information we can find length AB using the cosine rule:

Cosine Rule:

$c^2=a^2+b^2-2ab*cos(C)$

$AB=$ side $c$

$c^2=(1.2)^2+(0.6)^2-2(1.2)(0.6)cos(107^@)$

$c^2=1.44+0.36-1.44cos(107^@)=2.22=>c$

$->=sqrt(2.22)=1.49$ miles