# Question #ffc84

##### 2 Answers

At some point measurement has to be made. The calculations below

Gives the

#### Explanation:

The sum of the internal angles on a triangle is

By the properties of similar triangles and ratio of proportionality we can now determine the length of the sides

By ratio

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I discuss here a common method

It is not restricted to right angled triangle only.It is applicable when the given angles can be drawn with the help of compass and ruler.

#### Explanation:

**Construction**

- A straight line
#PQ=11 cm# is first drawn. - With the help of a pencil compass and a ruler then we draw
#/_YPQ=15^@ "and"/_YQP = 30^@# .As a result PY and QY intersect at Y - Again with the help of pencil compass and a ruler we draw
#/_PYO=15^@ "and"/_QYZ = 30^@# . As a result PO intersects PQ at O and YZ intersects PQ atZ #DeltaYOZ# is the required triangle drawn.

**Proof**

- In
#DeltaYPO,/_OYP=15^@=/_OPY# by construction, So#DeltaYPO# is an isosceles triangle whose#YO =PO# - In
#DeltaZYQ,/_ZYQ=30^@=/_ZQY# by construction, So#DeltaYPO# is an isosceles triangle whose#YZ =ZQ# - Now in
#DeltaYOZ,/_YOZ=/_OYP+/_OPY=30^@,"since"/_YOZ" is the exterior angle of" Delta PAB # , - Also in
#DeltaYOZ,/_YZO=/_ZYQ+/_YQZ=60^@,"since"/_YZO" is the exterior angle of" Delta QYZ # , - Hence in
#DeltaYOZ,/_YOZ=30^@,/_YZO=60^@ "and Perimeter=" YO+OZ+ZY = PO+OZ+ZQ=PQ =11 cm#