Suppose ABC is a right triangle with sides a b and c and rig

Suppose ABC is a right triangle with sides a, b, and c and right angle at C. Find the unknown side length using the the six trigonometric functions for angle B. a = 5, c = 6 The unknown side length b is. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

right angle is at C

a= 5 , c = 6

hypotenuse = 6

perpendicular = 5

applying pythagorean identity to find b

b^2 = c^2 - a^2

b^2 = 6^2 - 5^2

b^2 = 11

b = sqrt 11

unknown side is b = sqrt 11