In a triangle ABC - a -3- b -5- c -7- Find the angle opposite to C-A- 60B- 90C- 150-D- 120-

The correct option is D 120^∘We know from trigonometric ratios of half angles that tanA/2 =√((s b)(s c)/(s a)) Here we need angle opposite to c i.e., C. Semipe ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Half Angles

In a triangle...

Question

In a triangle ABC, a = 3, b = 5, c = 7. Find the angle opposite to C.

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120^{\circ}

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150^{\circ}

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Solution

The correct option is C $120^{\circ}$
We know from trigonometric ratios of half angles that $t a n \frac{A}{2} = \sqrt{\frac{(s - b) (s - c)}{(s - a)}}$
Here we need angle opposite to c i.e., C.
Semiperimeter, $S = \frac{a + b + c}{2} = \frac{3 + 5 + 7}{2} = \frac{15}{2}$
$t a n \frac{C}{2} = \sqrt{\frac{(s - b) (s - c)}{(s - a)}}$
$= \sqrt{\frac{(s - 3) (s - 5)}{(s - 7) s}} = \sqrt{\frac{(15 - 6) (15 - 10) (2)}{4 (15 - 14) (\frac{15}{2})}}$
$= \sqrt{\frac{9 (5)}{15}} = \sqrt{3} \Rightarrow \frac{C}{2} = 60^{\circ} \Rightarrow C = 120^{\circ}$

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