What is Trigonometry?
Trigonometry is a branch of Mathematics that studies the relationship between the angles and sides of a triangle.
The word Trigonometry comes from two Greek words that mean triangle and measurement. In Class 10, we mainly study these relationships using right-angled triangles.
Trigonometry helps us find unknown sides or angles of a right-angled triangle using known information.
The foundation of Trigonometry
A right-angled triangle is a triangle in which one angle is exactly 90°.
Know the three sides
Before learning sin, cos and tan, you must be able to identify the three sides of a right-angled triangle correctly.
Perpendicular
The side opposite the angle we are considering.
Base
The side next to the angle, excluding the hypotenuse.
Hypotenuse
The longest side, opposite the 90° angle.
Test Your Understanding
Finding Hypotenuse in a Right Triangle
In a right triangle ΔABC right-angled at B, if AB = 3 cm and BC = 4 cm, find the length of hypotenuse AC.
Solution:
By Pythagoras Theorem: AC² = AB² + BC²
AC = √25 = 5 cm
Finding Unknown Side Length
In right triangle ΔPQR right-angled at Q, hypotenuse PR = 13 cm and side PQ = 5 cm. Find base QR.
Solution:
By Pythagoras Theorem: PR² = PQ² + QR²
169 = 25 + QR² → QR² = 144
QR = √144 = 12 cm
What did we learn?
Trigonometry studies relationships between angles and sides of triangles.
Class 10 Trigonometry mainly deals with right-angled triangles.
The three important sides are perpendicular, base and hypotenuse.
The hypotenuse is always opposite the 90° angle.