Question

A triangle has sides A, B, and C. Sides A and B are of lengths `5` and `4`, respectively, and the angle between A and B is `(pi)/2`. What is the length of side C?

Answer 1

`color(violet)(c = sqrt (5^2 + 4^2) ~~ 6.4 " units"`

Explanation:

`:. c^2 = a^2 + b^2 - 2ab cos C`

`"Given : " a = 5, b = 4, hat C = pi/2`

`c^2 = 5^2 + 4^2 + (2 * 5 * 4 * cos (pi/2)) = 5^2 + 4^2`

as `cos (pi/2) = 0`

`color(violet)(c = sqrt (5^2 + 4^2) ~~ 6.4 " units"`