Question

Знайдіть HB, якщо CH - висота, АВ = 20 см​

Answer 1

$5 cm$

Объяснение:

$CH \perp AB \Rightarrow CH=\sqrt{AH \cdot HB} \Rightarrow AH \cdot HB=CH^{2} \Rightarrow HB=\dfrac{CH^{2}}{AH};$

$\angle A=30^{\circ} \Rightarrow CB=\dfrac{AB}{2} \Rightarrow CB=\dfrac{20}{2}=10 (cm);$

$AC^{2}+CB^{2}=AB^{2} \Rightarrow AC^{2}=AB^{2}-CB^{2} \Rightarrow AC=\sqrt{AB^{2}-CB^{2}};$

$AC=\sqrt{20^{2}-10^{2}}=\sqrt{400-100}=\sqrt{300}=10\sqrt{3};$

$\angle A=30^{\circ} \Rightarrow CH=\dfrac{AC}{2} \Rightarrow CH=\dfrac{10\sqrt{3}}{2}=5\sqrt{3} (cm);$

$AH=\sqrt{AC^{2}-CH^{2}} \Rightarrow AH=\sqrt{(10\sqrt{3})^{2}-(5\sqrt{3})^{2}}=\sqrt{300-75}=\sqrt{225}=$

$=15 (cm);$

$HB=\dfrac{(5\sqrt{3})^{2}}{15}=\dfrac{25 \cdot 3}{15}=\dfrac{25}{5}=5 (cm);$