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

right triangle 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.

right triangle in problem 1

Detailed Solution

Problem 2: In the figure below, find c.

right triangle in problem 2

Detailed Solution

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.

Detailed Solution

Problem 4: Find the exact values of x and y.

right triangle in problem 2

Detailed Solution

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.

Detailed Solution

More references on solving problems related to trigonometry and geometry.

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Updated: February 2015

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