First slide

Equation of line in Straight lines

Question

The vertices of the triangle $A B C$ are $A (1, 2),$ $B (0, 0)$ and $C (2, 3),$ then the greatest angle of the triangle is

Moderate

A

75°
B

105°
C

120°
D

None of these

Solution

Sides of the triangle are
$a = B C = \sqrt{4 + 9} = \sqrt{13}, b = \sqrt{2}, c = \sqrt{5}$
The greatest angle $A$ is given by
$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{2 + 5 - 13}{2 \times \sqrt{2} \times \sqrt{5}} = \frac{- 3}{\sqrt{10}}$ .

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