Determine 67754

Adam (A) stands on one river bank, and Bedrich (B) stands on the other. To determine their distance, the base AC with a length of 136 m and the angles CAB with a size of 70°21' and ACB with a size of 43°44' were measured on one river bank. What is the distance between Adam and Bedrich?

Correct answer:

AB =  102.8474 m

Step-by-step explanation:

$$\begin{gathered} AC=136\text{m} \\ CAB=70°21^{\prime }=70°+\frac{21}{60}°=70.35°=70.35 \\ ACB=43°41^{\prime }=43°+\frac{41}{60}°=43.6833°\doteq 43.6833 \\ \angle ABC=180-\angle CAB-\angle ACB=180-70.35-43.6833=\frac{1979}{30}\doteq 65.9667{}^{\circ } \\ \sin ACB:\sin ABC=AB:AC \\ AB=AC\cdot \frac{\sin ACB}{\sin ABC}=AC\cdot \frac{\sin 43.683333333333°}{\sin 65.966666666667°}=136\cdot \frac{\sin 43.683333333333°}{\sin 65.966666666667°}=136\cdot \frac{0.690672}{0.913309}=102.847=102.8474\text{m} \end{gathered}$$

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