You visited us 1 times! Enjoying our articles? Unlock Full Access!

Area of a Triangle

The perimeter...

Question

The perimeter of a $△ A B C$ is 3 times the arithmetic mean of sine of its angles.
If the side $^{'} b^{'} = 1$ , then find the angle $B$

\frac{π}{6}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{π}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{π}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{π}{2}$
$G i v e n :$
$s = 3 \frac{s i n A + s i n B + s i n C}{3} = s i n A + s i n B + s i n C$

Multiplying $2 R$ on both sides
$2 R s = 2 R (s i n A + s i n B + s i n C) . . . . . . . . . . . . . . . . . . . . . . . . . (1)$

we know that, $a = 2 R s i n A b = 2 R s i n B c = 2 R s i n C$

Putting these values in $(1)$ we get,
$2 R (a + b + c) = a + b + c \Rightarrow R = \frac{1}{2}$

Again from sine Rule,
$\frac{b}{s i n B} = 1 \Rightarrow s i n B = b$

Since, $b = 1$ (Given)
$s i n B = 1 \Rightarrow B = 90^{o}$

Therefore, Answer is $\frac{π}{2}$

Suggest Corrections

Similar questions

Δ

3

b = 1

B

△ A B C

6

a

1

A

5. If the perimeter of a triangle ABC is 6 times the Arithmetic mean of the sines of its angles. If the side 'a'is 1, then the angle A is?

\frac{π}{x}

x

x

Δ A B C

6

b

1

lim A \to C \frac{\sqrt{1 - 4 (2 - \sqrt{3}) sin A sin C}}{| A - C |}

Join BYJU'S Learning Program