Angles and Triangles- Prakash Kumar Sekar

Prakash Kumar S

Angles

An angle is the amount of rotation between two straight

lines. Angles may be measured either in degrees or in

radians.

If a circle is divided into 360 equal parts, then each part

is called 1 degree and is written as 1◦

1 revolution = 360◦

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Any angle between 0◦ and 90◦ is called an acute angle.

An angle equal to 90◦ is called a right angle.

Any angle between 90◦ and 180◦ is called an obtuse

angle.

Any angle greater than 180◦ and less than 360◦ is called a

reflex angle.

An angle of 180◦ lies on a straight line.

If two angles add up to 90◦ they are called

complementary angles.

If two angles add up to 180◦ they are called

supplementary angles.

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Finding Unknown Angles

a = c, b = d, e = g and f = h. Such

pairs of angles are called vertically

opposite angles.

(b) a = e, b = f , c = g and d = h.

Such pairs of angles are called

corresponding angles.

(c) c = e and b = h. Such pairs of

angles are called alternate angles.

(d) b + e = 180◦ and c + h = 180◦.

Such pairs of angles are called

interior angles.Prakash Kumar S

Radians and Minutes

1 degree = 60 minutes

50’ + 40’ = ?

θ = s/r = 2πr/r = 2π

2 = 360

= 180

1 radian = 180/

2 radian = ?

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Find alpha

Prakash Kumar S

Find alpha

X + Y = alpha

X + 137 = 180 ( interior angles )

Y = 16 (corresponding angles)

x

y

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Triangle

A triangle is a figure enclosed by three straight lines.

The sum of the three angles of a triangle is equal to 180◦

30 + 75 + 75 = 180

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Types of Triangles

An equilateral triangle is one in

which all the sides and all the

angles are equal

An isosceles triangle is one in

which two angles and two sides

are equal.

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Prakash Kumar S

Finding Angles, Sides and Distances

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Similar Triangles

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Find DB

Prakash Kumar S

Find DB

Similar Triangles

9/(9+6) = x/10

X = 6

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The theorem of Pythagoras

In any right-angled triangle, the square of the hypotenuse is

equal to the sum of the squares of the other two sides.

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Prakash Kumar S

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Find this on your Own

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A surveyor measures the angle of elevation of the top of a perpendicular

building as 19◦. He moves 120m nearer to the building and finds the

angle of elevation is now 47◦. Determine the height of the building

Sine and Cosine Rule

They are applicable for all type of triangle

Sine Rule

a/sinA = b/sinB = c/sinC

Cos Rule

a^2 = b^2 + C^2 – 2bc*cosA

Prakash Kumar S

Thank YouBy Prakash Kumar S

Prakash Kumar S