Question

9. Find the area of triangle ABC if angle A=60° and angle B=30° and AC=4

Answer 1

$\huge{ \green{ \mathfrak{ \underline{Question}}}}$

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

■☆Find the area of triangle ABC if angle A=60° and angle B=30° and AC=4☆■

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

$\huge{ \green{ \mathfrak{ \underline{Answer}}}}$

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

$\boxed{\red{\bold{By \:angle \: sum \:property}}}$

$\implies \angle A + \angle B + \angle C = 180^o$

$\implies 60^o + 30^o + \angle C = 180^o$

$\implies \angle C = 180^o - 90^o$

$\blue{\implies \angle C = 90^o}$

$\boxed{\red{\bold{By \:Trigonometric\: ratios:}}}$

$\implies tanC = \displaystyle{\frac{AC}{BC}}$

$\implies tan30^o = \displaystyle{\frac{4}{BC}}$

$\implies \displaystyle{\frac{1}{\sqrt{3}}} = \frac{4}{BC} \\ \left( \because tan30^o = \frac{1}{\sqrt{3}} \right)$

$\blue{\implies BC = 4 \sqrt{3} \:units}$

$\boxed{\red{\bold{Area \: of \: \triangle ABC:}}}$

$\purple{\implies \displaystyle{\frac{1}{2}}\: ×\: base\: × \:height}$

$\implies \displaystyle{\frac{1}{2}} × 4 × 4 \sqrt{3}$

$\green{\implies 8 \sqrt{3}\: square \: units}$

▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂

Answer 2

hope it helps!

#sumedhian ❤❤