It shows the different methods to calculate angles and sides in the different type of triangle. Its one of the basics for understanding doing surveying.

1. Angles and Triangles
- Prakash Kumar Sekar
Prakash Kumar S

2. 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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3. 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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4. 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

5. 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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6. Find alpha
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7. Find alpha
X + Y = alpha
X + 137 = 180 ( interior angles )
Y = 16 (corresponding angles)
x
y
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8. 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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9. 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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12. Finding Angles, Sides and Distances
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13. Similar Triangles
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14. Find DB
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15. Find DB
Similar Triangles
9/(9+6) = x/10
X = 6
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16. 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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19. 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

20. 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
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21. Thank You
By Prakash Kumar S
Prakash Kumar S