In triangle , ( B = 90^ ),

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

In triangle

ABC

\angle B = 90^{\circ}

AB = 5\,\text{cm}

BC = 12\,\text{cm}

and

AC = 13\,\text{cm}

. Taking

\angle C

as the reference angle, answer the following: (i) Identify the hypotenuse, the side opposite to

\angle C

, and the side adjacent to

\angle C

. (ii) Using the given side lengths, write the exact values of

\sin C

\cos C

and

\tan C

. (iii) Without carrying out any further calculation, explain why the value of

\cos C

must lie strictly between

0

and

1

for this triangle.