Question
In a right triangle ABC, right angled at C, if $\angle\text{B} = 60^\circ$ and AB = 15 units. Find the remaining angles and sides.
✓
Answer
In a $\triangle\text{le}$ sum of all angles = 180° $ \angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ $\Rightarrow90^\circ+60^\circ+\angle\text{A}=180^\circ$ $\angle\text{A}=180^\circ-150^\circ$ $\therefore \angle\text{A}=30^\circ$
From above figure $\cos\text{B}=\frac{\text{BC}}{\text {AB}}$ $\cos60^\circ=\frac{\text{BC}}{ {15}}$ $\frac{1}{2}=\frac{\text{BC}}{15}$ $\text{BC}=\frac{15}{2}$ $\sin\text{B}=\frac{\text{AC}}{15}$ $\sin60^\circ=\frac{\text{AC}}{15}$ $\frac{\sqrt{3}}{2}=\frac{\text{AC}}{15}\Rightarrow\text{AC}=\frac{15\sqrt{3}}{2}$
From above figure $\cos\text{B}=\frac{\text{BC}}{\text {AB}}$ $\cos60^\circ=\frac{\text{BC}}{ {15}}$ $\frac{1}{2}=\frac{\text{BC}}{15}$ $\text{BC}=\frac{15}{2}$ $\sin\text{B}=\frac{\text{AC}}{15}$ $\sin60^\circ=\frac{\text{AC}}{15}$ $\frac{\sqrt{3}}{2}=\frac{\text{AC}}{15}\Rightarrow\text{AC}=\frac{15\sqrt{3}}{2}$
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