angles and triangles
Post on 19-Jul-2015
782 Views
Preview:
TRANSCRIPT
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◦
Prakash Kumar S
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.
Prakash Kumar S
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 = ?
Prakash Kumar S
Find alpha
Prakash Kumar S
Find alpha
X + Y = alpha
X + 137 = 180 ( interior angles )
Y = 16 (corresponding angles)
x
y
Prakash Kumar S
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
Prakash Kumar S
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.
Prakash Kumar S
Prakash Kumar S
Prakash Kumar S
Finding Angles, Sides and Distances
Prakash Kumar S
Similar Triangles
Prakash Kumar S
Find DB
Prakash Kumar S
Find DB
Similar Triangles
9/(9+6) = x/10
X = 6
Prakash Kumar S
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.
Prakash Kumar S
Prakash Kumar S
Prakash Kumar S
Find this on your Own
Prakash Kumar S
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
top related