# Solve Problems Using Trigonometric Ratios

 A set of problems, that may be solved using the trigonometric ratios, is presented. Also detailed solutions are presented in a separate page. Definition of Trigonometric Ratios In a right triangle, the six trigonometric ratios; the sine ratio, the cosine ratio, the tangent ratio, the cosecant ratio, the secant ratio and the cotangent ratio are defined as follows: 1 - The sine of angle A = sin (A) = side opposite angle A / hypotenuse = a / c 2 - The cosine of angle A = cos (A) = side adjacent to angle A / hypotenuse = b / c 3 - The tangent of angle A = tan (A) = side opposite angle A / side adjacent to angle A = a / b 4 - The secant of angle A = sec (A) = hypotenuse / side adjacent to angle A = c / b 5 - The cosecant of angle A = csc (A) = hypotenuse / side opposite to angle A = c / a 6 - The cotangent of angle A = cot (A) = side adjacent to angle A / side opposite angle A = b / a Problem 1: Given the right triangle below, find sin A, cos A, tan A, sec A, csc A and cot A. Problem 2: In the figure below, find c. Problem 3: If x is an acute angle of a right triangle and sin x = 3 / 7, find the exact value of the trigonometric functions cos x and cot x. Problem 4: Find the exact values of x and y. Problem 5: If x is an acute angle and tan x = 5, find the exact value of the trigonometric functions sin x and cos x. More references on solving problems related to trigonometry and geometry.