LABELLING RIGHT ANGLED TRIANGLES

What is right triangle ?

A right angled triangle is a triangle with one of the angles as 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle 

In a right triangle,

• The side which is opposite to 90 degree is known as hypotenuse

• The side which is opposite to theta is known as opposite side.
• The side left over is known as adjacent side.

Problem 1:

In the diagrams below, name the:

i) Hypotenuse

ii)  Side opposite the angle marked θ

iii) Side adjacent to the angle marked θ.

a.

Solution :

i) Hypotenuse = AB (opposite to 90 degree)

ii)  Side opposite the angle marked θ = BC

iii) Side adjacent to the angle marked θ = AC

Problem 2 :

Solution :

i) Hypotenuse = RQ

ii) Side opposite the angle marked θ = PR

iii)  Side adjacent to the angle marked θ = PQ

Problem 3 :

Solution :

i) Hypotenuse = XZ

ii) Side opposite the angle marked θ = YZ

iii)  Side adjacent to the angle marked θ = XY

Problem 4 :

The right angled triangle alongside has hypotenuse of length a units and other sides of length b units and c units. θ and Φ are the two acute angles. Find the length of the side:

a)   Opposite θ

b)   Opposite Φ

c)   Adjacent to θ

d)   Adjacent to Φ

Solution :

a)   Opposite θ = b

b)   Opposite Φ = c

c)   Adjacent to θ = c

d)   Adjacent to Φ = b

Problem 5 :

Given the right angle triangle shown here:

state the length of :

1) the side opposite angle a

2) the side opposite angle b

3) the hypotenuse

4) the side adjacent to angle b 

5) the side adjacent to angle a

Solution :

1) the side opposite angle a = 4

2) the side opposite angle b = 3

3) the hypotenuse = 5

4) the side adjacent to angle b = 4  

5) the side adjacent to angle a = 3

Problem 6 :

Given the right angle triangle ABC shown here

name the:

1) Hypotenuse

2) Adjacent side to b

3) Opposite side to a

4) Opposite side to b

5) Adjacent side to a

Solution :

1) Hypotenuse = AB

2) Adjacent side to b = BC

3) Opposite side to a = BC

4) Opposite side to b = AC

5) Adjacent side to a = AC