Question

Two boats start their journey from the same point A and travel along directions AC and AD, as shown below:

Answer 1

In triangle ABD, $\angle D$ = 30°

Applying trigonometry,

$\boxed {\mathrm{ \tan(30) = \dfrac{ AB}{BD} }}$

• $\dfrac{1}{ \sqrt{3} } = \dfrac{100}{BD }$

• $BD = 100 \sqrt{3}$

Now, In triangle ABC, $\angle C$ = 60°

Applying trigonometry,

$\boxed{ \mathrm{ \tan(60) = \frac{AB}{BC} }}$

• $\sqrt{3} = \dfrac{100}{BC}$

• $BC = \dfrac{100}{ \sqrt{3} }$

Measure of CD = BD - BC

• $CD = 100 \sqrt{3} - \dfrac{100}{ \sqrt{3} }$

• $CD = \dfrac{300 - 100}{ \sqrt{3} }$

• $CD = \dfrac{200}{ \sqrt{3} }$

• $CD = 115.47 \: \: ft$

• $\boxed {\mathrm{CD \approx115.5 \: \: ft}}$

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