As shown in the diagram, a cottage is located at C on an island in the lake, and a marine is located at B. If the distance from A to D is 10.0 km, and <ABC = <CAB = 28˚, find the distance from B to C.

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- Jun 12th 2007, 01:24 PM #1

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- Jun 12th 2007, 06:14 PM #2

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Hello, Ph4m!

As shown in the diagram, a cottage is located at C on an island in the lake,

and a marine is located at B.

If the distance AD = 10.0 km, and <ABC = <CAB = 28°, find distance BC.Code:A * * ** * * * * 28° * * * * * 10.0 km * *x * * * * * 28° 124° * 56° * * * * * * * * * * * * * * B x C D

Since $\displaystyle \angle ABC = \angle CAB = 28^o$, triangle ABC is isosceles.

Hence: .$\displaystyle AC = BC = x$.

Since $\displaystyle \angle ACB \:= \:180^o - 28^o - 28^o \:=\:124^o$, then: .$\displaystyle \angle ACD = 56^o$

In right triangle ADC, we have: .$\displaystyle \sin56^o \:=\:\frac{10}{x}\quad\Rightarrow\quad x \:=\:\frac{10}{\sin56^o} \:=\:12.06217949$

Therefore: .$\displaystyle BC \:\approx\:12.1$ km.