Question

In the diagram, AC = 12 V3. Find BC and AB. Write your answers in simplest form.B60930O BC = 72. AB = 36O BC = 36. AB = 72O BC = 24, AB = 12O BC = 12. AB = 24

Answer 1

constructing the triangle

From the figure,

We will be applying trig. ratios

$\text{SOH CAH TOA}$

Finding BC with respect to angle 30

$\begin{gathered} \text{Tan 30 = }\frac{opp}{adj} \\ \text{Tan 30 = }\frac{BC}{12\sqrt[]{3}} \\ \text{cross multiply} \\ BC\text{ = Tan 30 }\times12\sqrt[]{3} \\ BC\text{ = }\frac{\sqrt[]{3}}{3}\text{ }\times\text{ 12}\sqrt[]{3} \\ BC\text{ = }\sqrt[]{3\text{ }}\text{ }\times\text{ 4}\sqrt[]{3} \\ BC\text{ = 4 }\times3 \\ BC\text{ = 12} \end{gathered}$

Finding AB with respect to angle 30

$\begin{gathered} \cos \text{ 30 = }\frac{adj}{hyp} \\ \cos \text{ 30 = }\frac{12\sqrt[]{3}}{AB} \\ \text{cross multiply} \\ \cos \text{ 30 }\times\text{ AB = 12}\sqrt[]{3} \\ \text{divide both sides by cos30} \\ AB\text{ = }\frac{12\sqrt[]{3}}{\cos \text{ 30}} \\ AB\text{ = }\frac{12\sqrt[]{3}}{\frac{\sqrt[]{3}}{2}} \\ AB\text{ = 12}\sqrt[]{3}\text{ }\times\text{ }\frac{2}{\sqrt[]{3}} \\ AB\text{ = 12 }\times2 \\ AB\text{ = 24} \end{gathered}$

Therefore,

BC = 12 and AB = 24