Trigonometry is the part of mathematics in which we learn to find the base, height & angles in a triangle. It is used in different fields where we use triangular shapes.

2. How to identify base perpendicular and hypotenuse in trigonometry?

3. How to find the base perpendicular and hypotenuse?

4. What is the ratio in trigonometry?

5. How to find the ratios in trigonometry?

## 1. What is perpendicular base and hypotenuse in trigonometry?

### a) What is perpendicular in trigonometry?

*90Âº*angle to each other. One of them is known as the Perpendicular or height of a right triangle.

### b) What is a base in a triangle?

*90Âº*angle with the perpendicular or height of the triangle.

### c) What is a hypotenuse in trigonometry?

*90Âº*angle.

## 2. How to identify base perpendicular and hypotenuse in trigonometry?

**a) How to identify a perpendicular in the triangle?**

**perpendicular**as shown by the arrow.

**b) How to identify the base in the triangle?**

**base**makes a 90Âº angle with perpendicular as shown by the blue colour in the above picture.

### c) How to identify a *hypotenuse* in the triangle?

**hypotenuse**in the right triangle. It is opposite to the 90Âº angle.

## 3. How to find the base perpendicular and hypotenuse?

__PYTHAGORAS THEOREM:__In a right-angled triangle square of its Hypotenuse is equal to the sum of the square of its Base and Perpendicular.

**H² = P² + B²**

a) How to find a Base in trigonometry?

Base²= Hypotenuse²- Perpendicular²

Base**²** = Hypotenuse**²** - Perpendicular**²**

Putting all the given values-

(Base)² = (5)² - (4)²

(Base)² = 25 - 16

(Base)² = 9

(Base)² = 3²

Base = 3cm

b) How to find perpendicular in trigonometry?

Perpendicular² =Hypotenuse²- Base²

**Let we have Hypotenuse = 13cm, Base = 5cm**

Perpendicular**² = **Hypotenuse**²** - Base**²**

Putting all the given values-

(Perpendicular)² = (13)² - (5)²

(Perpendicular)² = 169 - 25

(Perpendicular)² = 144

(Perpendicular)² = 12²

Perpendicular = 12cm

c) How to find hypotenuse in trigonometry?

Hypotenuse²= Perpendicular²+ Base²

**Let's take an example for a better understanding. We have Perpendicular = 8cm, Base = 6cm**

Hypotenuse**²** = Perpendicular**²** + Base**²**

Putting all the given values-

(Hypotenuse)² = (8)² + (6)²

(Hypotenuse)² = 64 + 36

(Hypotenuse)² = 100

(Hypotenuse)² = 10²

Hypotenuse = 10cm

## 4. What is the ratio in trigonometry?

**SinÎ¸ = Perpendicular/Hypotenuse**

*According to the picture-*

*SinÎ¸ = (PQ / PR) or (BC / AC)*

**CosecÎ¸ = Hypotenuse/Perpendicular**

*The ratio of cosec is the inverse of sin.*

*According to the picture-*

*CosecÎ¸ = (PR / PQ) or (AC / BC)*

**CosÎ¸ = Base/Hypotenuse**

*According to the picture-*

*CosÎ¸ = (QR / PR) or (AB / AC)*

**SecÎ¸ = Hypotenuse/Base**

*According to the picture-*

*SecÎ¸ = (PR / QR) or (AC / AB)*

**TanÎ¸ = Perpendicular/Base**

*According to the picture-*

*TanÎ¸ = (PQ / QR) or (BC / AB)*

**CotÎ¸ = Base/Perpendicular**

*The ratio of the cot is the inverse of tan.*

*According to the picture-*

*CotÎ¸ = (QR / PQ) or (AB / BC)*

## 5. How to find the ratios in trigonometry?

**Example:-**

**H² = P² + B²**

*Perpendicular(BC) = 3cm,*

*Base(AB) = 4cm &*

*Hypotenuse(AC) = 5 cm*.

*SinÎ¸ = P/H*

*= BC / AC*

*= 3 / 5*

*CosecÎ¸ = H/P*

*= AC / BC*

*= 5 / 3*

*CosÎ¸ = B/H*

*= AB / AC*

*= 4 / 5*

*SecÎ¸ = H/B*

*= AC / BC*

*= 5 / 4*

*TanÎ¸ = P/B*

*= BC / AB*

*= 3 / 4*

*CotÎ¸ = B/P*

*= AB / BC*

*= 4 / 3*