The angles A- B- and C of a triangle are in A-P- and b - c -3- 2- then - A -A- 60-B- 75-C- 30-D- 45-

The correct option is B 75°Since angles A, B and C are in A.P., ∴ nbsp;2∠B=∠A+∠C⇒3∠B=∠A+∠B+∠C⇒∠B=60°Now,bsin nbsp;B=csin nbsp;C⇒bc=sin nbsp;Bsin nbsp; ...

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Byju's Answer

Standard XII

Mathematics

Sine Rule

The angles A,...

Question

The angles A, B, and C of a triangle are in A.P. and
b:c = $\sqrt{3} : \sqrt{2}, t h e n ∠ A =$ .

60 °

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75 °

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30 °

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45 °

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Solution

The correct option is B $75 °$
Since angles A, B and C are in A.P.,
$∴ 2 ∠ B = ∠ A + ∠ C \Rightarrow 3 ∠ B = ∠ A + ∠ B + ∠ C \Rightarrow ∠ B = 60 ° Now, \frac{b}{sin B} = \frac{c}{sin C} \Rightarrow \frac{b}{c} = \frac{sin B}{sin C} \Rightarrow \frac{\sqrt{3}}{\sqrt{2}} = \frac{sin 60 °}{sin C} \Rightarrow sin C = \frac{1}{\sqrt{2}} ∠ C = 45 °$ $∴ ∠ A = 180 ° -(60 ° + 45 °) = 75 °$

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Similar questions

Q. In a triangle ABC,

∠ A = 60 ° a n d b : c = \sqrt{3} + 1 : 2, t h e n t h e v a l u e o f ∠ B - ∠ C =

Q. In ∆ABC, ∠A : ∠B : ∠C = 3 : 2 : 1 and CD ⊥ AC. Then, ∠ECD = ?
(a) 60°
(b) 45°
(c) 75°
(d) 30°

Q. The angles

A, B

and

C

of a triangle

A B C

are in

A . P .

b : c = \sqrt{3} : \sqrt{2}

, then the angle

A

Q. In triangle

A B C

, if

A, B, C

are in A.P. and

b : c = \sqrt{3} : \sqrt{2}

, then find

A, B, C

Q. Suppose the angles of a triangle

A B C

are in

A . P

and sides

b

and

c

satisfy

b : c = \sqrt{3} : \sqrt{2}

then the angle

A

equals ?

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The angles A, B, and C of a triangle are in A.P. and b:c = √3:√2, then ∠A= .

The correct option is B 75°Since angles A, B and C are in A.P., ∴ 2∠B=∠A+∠C⇒3∠B=∠A+∠B+∠C⇒∠B=60°Now,bsin B=csin C⇒bc=sin Bsin C⇒√3√2=sin 60°sin C⇒sin C=1√2∠C=45°∴∠A=180°−(60°+45°) = 75°

The angles A, B, and C of a triangle are in A.P. and
b:c = $\sqrt{3} : \sqrt{2}, t h e n ∠ A =$ .