In triangle ABC if a-2- b-3 and tan A-3-5 and the two possible values of the side c are K1-10 and K2-10- then K1 and K2 are equal to-

The correct options are A K_1 = 1 and K_2 = 12 B K_1 = 12 and K_2 = 1 tan A =√( 3 5 #160; ) #10;⇒cos A =√( 5 8 #160 ...

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Standard XII

Mathematics

Integration by Parts

In triangle ...

Question

In triangle $A B C$ if $a = 2, b = 3$ and $tan A = \sqrt{\frac{3}{5}}$ and the two possible values of the side $c$ are $K_{1} \sqrt{10}$ and $K_{2} \sqrt{10}$ , then $K_{1}$ and $K_{2}$ are equal to?

K_{1} = 1

and

K_{2} = \frac{1}{2}

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K_{1} = \frac{1}{2}

and

K_{2} = 1

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

K_{1} = \frac{1}{2}

and

K_{2} = \frac{1}{2}

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K_{1} = 1

and

K_{2} = 2

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Solution

The correct options are
A $K_{1} = 1$ and $K_{2} = \frac{1}{2}$
B $K_{1} = \frac{1}{2}$ and $K_{2} = 1$
$tan A = \sqrt{\frac{3}{5}} \Rightarrow cos A = \sqrt{\frac{5}{8}} cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} \sqrt{\frac{5}{8}} = \frac{9 + c^{2} - 4}{6 c} \sqrt{8} c^{2} - 6 \sqrt{5} c - 4 \sqrt{8} = 0 8 c^{2} - 6 \sqrt{40} c - 32 = 0 2 c^{2} - 3 \sqrt{10} c - 8 = 0 c = \sqrt{10}, \frac{\sqrt{10}}{2}$

So options $A$ and $B$ are correct

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Similar questions

Q. Find the value of

k_{1}

and

k_{2}

for which

\to V

can be represented as

\to V = k_{1} \to A + k_{2} \to B

. Where,

\to V = 2 i - j

\to A = 3 i - 2 j

and

\to B = 3 i + 3 j .

Equilibrium constants $K_{1}$ and $K_{2}$ for the following equilibria are

$N O (g) + 0.5 O_{2} (g) \to K_{1} N O_{2} (g)$ and
$2 N O_{2} (g) \to K_{2} 2 N O (g) + O_{2} (g)$

Q. Two gaseous equilibria

S O_{2} (g) + \frac{1}{2} O_{2} (g) ⇌ S O_{3} (g)

and

2 S O_{3} (g) ⇌ 2 S O_{2} (g) + O_{2} (g)

have equilibrium constants

K_{1}

and

K_{2}

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298 K

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is correct:

Two gaseous equilibria $S O_{2} (g) + 0.5 O_{2} (g) ⇌ S O_{3} (g)$ and

$2 S O_{3} (g) ⇌ 2 S O_{2} (g) + O_{2} (g)$ have equilibrium constants $K_{1}$ and $K_{2}$ respectively

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respectively.

S O_{2} (g) + \frac{1}{2} O_{2} (g) ⇌ S O_{3} (g)

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In triangle ABC if a=2,b=3 and tanA=√35 and the two possible values of the side c are K1√10 and K2√10, then K1 and K2 are equal to?

The correct options are A K1=1 and K2=12 B K1=12 and K2=1tanA=√35⇒cosA=√58cosA=b2+c2−a22bc√58=9+c2−46c√8c2−6√5c−4√8=08c2−6√40c−32=02c2−3√10c−8=0c=√10,√102 So options A and B are correct

In triangle $A B C$ if $a = 2, b = 3$ and $tan A = \sqrt{\frac{3}{5}}$ and the two possible values of the side $c$ are $K_{1} \sqrt{10}$ and $K_{2} \sqrt{10}$ , then $K_{1}$ and $K_{2}$ are equal to?