90 Degree Right Angle

In geometry and trigonometry, a right angle is an angle that bisects the angle formed by two halves of a straight line. More precisely, if a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.
A right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90 degree angle).



The side opposite the right angle is called the hypotenuse (side c in the figure above). The sides adjacent to the right angle are called legs. (Source: from Wikipedia).It is shown in the figure.
Now, we are going to see some of the problems involving 90 degree right angle. From these problems, we can get clear view about 90 degree right angle.

90 degree right angle problems:

Example problem 1:
Using the diagram shown, Find the length of hypotenuse.

Given:

Right angle triangle

 a = 5cm and b = 5cm

Use the Pythagorean Theorem to find c.

c² = a² + b²

Substitute a = 5 and b = 5.

c² = 5² + 5²

c²=25+25

c²=50

Find the square root of each side.

C= √50=5 √2cm

Additional problems in 90 degree right angle:

Example problem 2:
Determine the length of the hypotenuse in the right angle triangle, given that angle θ = 37 degree.

Solution:

Sin θ= opposite side / hypotenuse

Sin 37 = 12 / x

0.6 = 12 / x

x = 12 / 0.6

x = 20

So, the side AC is 20cm.

Example problem 3:
Determine the length of the side x in the diagram, given that angle θ = 60 degree.

Solution:

Here, we use the sin θ. because the sin θ is related to the opposite side and hypotenuse.

Sin θ= opposite side / hypotenuse

Sin 60 = x / 24

0.866 = x / 24

x = 24* 0.866

x = 20.8

So, the side AC is 20.8cm.

Practice problems in right angle:
1) Find the length of hypotenuse when the adjacent side is 5 and the opposite side is 12. (Answer: hypotenuse=13)
2) Determine the length of the opposite side, given that angle θ = 30 degree and hypotenuse is 24. (Answer: opposite side= 12).