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P-2 Pythagoras Theorem — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsP-2 Pythagoras Theorem2 Marks
Question
See fig 2.11. In $\triangle \mathrm{ABC}, \angle \mathrm{B}=90^{\circ}, \angle \mathrm{A}=30^{\circ}, \mathrm{AC}=14$, then find $\mathrm{AB}$ and $\mathrm{BC}$

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Answer

In $\triangle \mathrm{ABC}$,
$\angle \mathrm{B}=90^{\circ}, \angle \mathrm{A}=30^{\circ}, \therefore \angle \mathrm{C}=60^{\circ}$
By $30^{\circ}-60^{\circ}-90^{\circ}$ theorem,
$\mathrm{BC}=\frac{1}{2} \times \mathrm{AC}$
$\mathrm{BC}=\frac{1}{2} \times 14$
$\mathrm{BC}=7$
$\mathrm{AB}=\frac{\sqrt{3}}{2} \times \mathrm{AC}$
$\mathrm{AB}=\frac{\sqrt{3}}{2} \times 14$
$\mathrm{AB}=7 \sqrt{3}$

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