that as A increases from ° to °, sin A increases from to and cos A decreases from to . Let us illustrate the use of the values in the table above through some examples. Example : In ABC, right-angled at B, AB = cm and ACB = ° (see Fig. .
). Determine the lengths of the sides BC and AC. Solution : To find the length of the side BC, we will choose the trigonometric ratio involving BC and the given side AB. Since BC is the side adjacent to angle C and AB is the side opposite to angle C, therefore BC = tan C BC = tan ° = which gives BC = cm Fig.
. To find the length of the side AC, we consider sin ° = AB = AC = cm Note that alternatively we could have used Pythagoras theorem to determine the third side in the example above, AC = ( ) cm = 10cm. Example : In PQR, right-angled at Q (see Fig. .
), PQ = cm and PR = cm. Determine QPR and PRQ. Solution : Given PQ = cm and PR = cm. Therefore, PR = sin R or sin R = So, PRQ = ° and therefore, QPR = °.
You may note that if one of the sides and any other part (either an acute angle or any side) of a right triangle is known, the remaining sides and angles of the triangle can be determined. Example : If sin (A – B) = , cos (A + B) = , ° < A + B °, A > B, find A and B. Solution : Since, sin (A – B) = , therefore, A – B = ° ( ) Also, since cos (A + B) = , therefore, A + B = ° ( ) Solving ( ) and ( ), we get : A