Answer to Question #191428 in Geometry for Robin

Question

in a triangle with the side lengths 5, 7, 9 length units, the largest angle x is

A) x>90

B) x=90

C) x<90

Answer 1

We have given the sides of triangle $5,7,9.$

Largest angle would be on the opposite of largest side,

We know,

$cosA = \dfrac{b^2+c^2-a^2}{2bc}$

$cosA = \dfrac{5^2+7^2-9^2}{2 \times 5 \times 7}$

$cosA = -\dfrac{21}{70}$

$A = 107.45^{\circ}$

Hence the angle will be greater than $90^{\circ}$