Question

Abc is a right triangle right angled at
c. if a=30 degree and ab=40 units,find the remaining two sides and angle b

Answer 1

acb is a right angled
ac/ab=cosa=√3/2
ac=40*√3/2=20√3cm............(1)(ans)
bc/ab=sin30=1/2
bc=(1/2)*40=20 cm...............((2))(ans)
angle b=180-(90+30)=60

Answer 2

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We have,

∠A = 30°

∠C = 90°

AB = 40 Units.

∠A + ∠B + ∠C = 180°

30° + ∠B + 90° = 180°

∠B = 180° - 120°

∠B = 60°

Cos A = adjacent / hypotenuse ⇒ AC/AB

Cos 30° = AC/40

√3/2 = AC/40

AC = √3/2 × 40

AC = 20√3 Units.

And,

Sin A = Opposite / Hypotenuse ⇒ BC/AB

Sin 30° = BC/40

1/2 = BC/40

BC = 40×1/2

BC = 20 Units.

Hence, AC = 20√3 Units,

BC = 20 Units

And

∠B = 60°.

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