Question

CРОЧНО!!! У трикутнику АВС ∠С = 90°. Знайдіть:

Answer 1

$\displaystyle\bf\\1)\\\\BC=8 \ \ \ , \ \ \ CosB=\frac{1}{2} \\\\CosB=\frac{BC}{AB} \\\\AB=\frac{BC}{CosB} =8:\frac{1}{2}=8\cdot 2=16\\\\\boxed{AB=16}\\\\\\2)\\\\AC=10 \ \ \ , \ \ \ SinB=0,25\\\\SinB=\frac{AC}{AB} \\\\AB=\frac{AC}{SinB}= 10:0,25=10\cdot4=40\\\\\boxed{AB=40}\\\\\\3)\\\\AB=6 \ \ \ , \ \ \ SinA=\frac{1}{3}\\\\SinA=\frac{BC}{AB} \\\\BC=AB\cdot SinA=6\cdot \frac{1}{3} =2\\\\\boxed{BC=2}$

$\displaystyle\bf\\4)\\\\AB=20 \ \ \ , \ \ \ CosA=0,4\\\\CosA=\frac{AC}{AB}\\\\AC=AB\cdot CosA=20\cdot 0,4=8\\\\\boxed{AC=8}\\\\\\5)\\\\AC=12 \ \ \ , \ \ \ tgA=\frac{3}{4} \\\\tgA=\frac{BC}{AC} \\\\BC=AC\cdot tgA=12\cdot \frac{3}{4}=9\\\\\boxed{BC=9}$