Question

28. In the adjoining figure, ABC is a right-angled
triangle in which ZB = 90°, ZA = 30° and AC = 20 cm
Find (i) BC, (ii) AB.​

Answer 1

Given:

• ABC is a right-angled triangle
• ∠B = 90°
• ∠A = 30°
• ∠C = 20cm

To Find:

1) BC

2) AB

Solution:

1) here,

$\large \sf \: \sin30 = \frac{BC}{AC}$

$\implies\large \sf \: \frac{1}{2} = \frac{BC}{20}$

⊱ $\sf\underline\red{BC\: = \:10cm}$

2) By Pythagoras theorem:

$\sf \: {(AB)}^{2} = ({AB})^{2} \: - ({BC})^{2}$

$\implies \sf \: ( {20})^{2} - ({10})^{2}$

$\implies \sf \: 300cm$

⊱ $\sf \underline \red {AB = 10 \sqrt{3cm} }$

Hence,

➙ BC = 10cm

➙ AB = 10√3cm