If-sin-B-C- -3-2-and-sin-A - 1-2- find B-C-and-A- B-C-60-and-A-30-B-C - 30-and-A-30-B-C-45-and-A-60-B-C-60-and-A-60-

The correct option is A B+C=60^∘ and A=30^∘ nbsp;The sine values for some specific acute angles are given below, [ nbsp; θ amp; 0^∘ amp; 30^∘ amp ...

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Standard X

Mathematics

Standard Angles

If sin(B+C)= ...

Question

$I f s i n (B + C) = \frac{\sqrt{3}}{2} a n d s i n A = \frac{1}{2}$ , find $B + C a n d A$ .

$B + C = 60^{\circ} a n d A = 30^{\circ}$

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$B + C = 30^{\circ} a n d A = 30^{\circ}$

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$B + C = 45^{\circ} a n d A = 60^{\circ}$

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$B + C = 60^{\circ} a n d A = 60^{\circ}$

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Solution

The correct option is A
$B + C = 60^{\circ} a n d A = 30^{\circ}$

The sine values for some specific acute angles are given below,
$\begin{matrix} θ & 0^{\circ} & 30^{\circ} & 45^{\circ} & 60^{\circ} & 90^{\circ} s i n θ & 0 & \frac{1}{2} & \frac{1}{\sqrt{2}} & \frac{\sqrt{3}}{2} & 1 \end{matrix}$

From the above table, we can see that $B + C = 60^{\circ}$ and $A = 30^{\circ} .$

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Similar questions

Choose the correct option and justify your choice.

(i)

(A). sin60°

(B). cos60°

(C). tan60°

(D). sin30°

(ii)

(A). tan90°

(B). 1

(C). sin45°

(D). 0

(iii) sin2A = 2sinA is true when A =

(A). 0°

(B). 30°

(C). 45°

(D). 60°

(iv)

(A). cos60°

(B). sin60°

(C). tan60°

(D). sin30°

Q. In an isosceles triangle ABC if AC = BC and AB² = 2AC², then ∠C =
(a) 30°
(b) 45
(c) 90°
(d) 60°

Q. In an isosceles ∆ABC, if AC = BC and AB² = 2AC², then ∠C = ?
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Q. If

\sin (A - B) = \frac{1}{2} and \cos (A + B) = \frac{1}{2}, 0 ° < (A + B) \leq 90 ° and A > B

then values of A and B are
(a) (60°, 30°)
(b) (60°, 15°)
(c) (45°, 15°)
(d) (60°, 25°)

Q. If

s i n (B + C) = \frac{\sqrt{3}}{2}

and

s i n A = \frac{1}{2}

, find

B + C

and

A

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If sin(B+C)=√32 and sin A=12, find B+C and A.

The correct option is A B+C=60∘ and A=30∘ The sine values for some specific acute angles are given below, θ0∘30∘45∘60∘90∘sinθ0121√2√321 From the above table, we can see that B+C=60∘ and A=30∘.

$I f s i n (B + C) = \frac{\sqrt{3}}{2} a n d s i n A = \frac{1}{2}$ , find $B + C a n d A$ .