If the lengths of the sides of triangle are 3,5 , and 7 , then the largest angle of the triangle is

Question

If the lengths of the sides of triangle are 3,5 , and 7 , then the largest angle of the triangle is (A) (π/2) (B) (5 π/6) (C) (2 π/3) (D) (3 π/4)

Tardigrade Admin · Accepted Answer

Let a=3, b=5, c=7. Then the largest angle is opposite to the longest side, i.e., angle C. Therefore, cos C=(a2+b2-c2/2 a b) =(9+25-49/2 × 3 × 5)=(-1/2) or C=(2 π/3)

Q. If the lengths of the sides of triangle are $3, 5$ , and $7$ , then the largest angle of the triangle is

$\frac{π}{2}$

$\frac{5 π}{6}$

$\frac{2 π}{3}$

$\frac{3 π}{4}$

Let $a = 3, b = 5, c = 7$ .
Then the largest angle is opposite to the longest side, i.e., $∠ C$ .
Therefore, $cos C = \frac{a ^{2} + b ^{2} - c ^{2}}{2 ab}$
$= \frac{9 + 25 - 49}{2 \times 3 \times 5} = \frac{- 1}{2}$
or $C = \frac{2 π}{3}$

Q. If the lengths of the sides of triangle are 3,5 , and 7 , then the largest angle of the triangle is

2π​

65π​

32π​

43π​