Question

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Answer 1

$\huge{\underline{\underline{Answer\::-}}}$

$\underline{\underline{Given\:-}}$

• $\angle BAC =$ 90°

• $\angle B : \angle C$ = 1 : 2

• AC = 4 cm

(consider attached picture for further reference)

$\underline{\underline{Solution\::-}}$

♦ As from the diagram we can See these Points

• BC is the Hypotenuse

• AC is Perpendicular

• AB is Base

>> Also Provided that ratio of $\angle B : \angle C$ = 1 : 2

♦ Let the common divisor of ratio be x

>>Then from angle sum property of Triangle

x + 2x + 90° = 180°

=> 3x = 180° - 90°

=> 3x = 90°

=> x = 30°

♦Now we know All the angles

Angle B = 30°(x)

Angle C = 60° (2x)

Angle A = 90° (given).

♦ As we know that :-

Sin∅ = $\dfrac{Perpendicular}{Hypotenuse}$

Sin 30° = $\dfrac{1}{2}$

♦ Now by using Sin∅ for angle B

Sin 30 ° = $\dfrac{Perpendicular}{Hypotenuse}$

=> $\dfrac{1}{2}$ = $\dfrac{AC}{BC}$

=> $\dfrac{1}{2}$ = $\dfrac{4}{BC}$

>> By cross multiplication

=> 1 (BC) = 4(2)

=> BC = 8

So the length of BC = 8cm