
Geometry
 Triangle Problems and Solutions 


Triangle, solved problems, examples 





Example:
In a triangle one angle a = 70°, find the obtuse angle formed by angle bisectors of other two
angles of the triangle. 
Solution: Given a = 70°.
j
= ? 

Example:
Lengths of two sides of a triangle are
13 cm and
15 cm, the altitude of the third side is
12 cm,
find the area of the
triangle. 
Solution: Given,
a =
13, b
= 15 and h_{c}
= 12.
A_{D}
=
? 


Example:
If in a triangle tana
= 2/3 and g
= 135°
then, tanb
is? 
Solution: Given,
tana
= 2/3 and g
= 135°.
tanb
= ? 

Example:
In a right triangle, with legs,
a
and b, inscribed is square such that one of its vertexes coincides
with the vertex of
the right angle, find the side of the square. 
Solution:
Given,
a
and b.
x
=
? 

Example:
In a scalene triangle side b = 6 and
c = 28 while
sina =
12/13 (a is the acute angle opposite to side
a), find the side
a. 
Solution:
Given,
b = 6,
c = 28
and sin a =
12/13.
a
=
?
Use of the cosine law. 



Example:
In a triangle side a
= Ö3
, side b
= Ö2
and angle a
= 60°, find angle b. 
Solution: Given,
a =
Ö3 ,
b = Ö2 and
a =
60°.
b
=
? Use of the sine
law. 


Example:
In a right triangle given are area A
and the angle
a
opposite to the leg a, find the leg
a. 
Solution:
Given, A
and a.
a
=
? 

Example:
Legs of a right triangle are a = 4 and
b
= 3. The distance of the center
of the inscribed circle from the vertex B
is? 
Solution:
Given, a = 4 and
b
= 3.
d(BS)
=
? 

Example:
Find the size of the angle that bisectors of the exterior angles on the hypotenuse of a right
triangle make. 
Solution:
An angle supplementary to an angle of a
triangle is called an exterior angle of the triangle. 

The exterior angle is equal to the
sum of interior angles, not supplementary, 



Example:
Over the diameter of a circle of radius r
= 6 cm constructed is an equilateral triangle with the side
a =
12 cm, find the area of the part of the triangle outside the circle. 
Solution:
Given, r
= 6 and a
= 12.
A
=
? 


Example:
Find the biggest angle of a triangle with sides of, 5
cm, 4
cm and 2
cm. 
Solution: Given,
a = 5,
b = 4 and
c = 2 .
a
=
?
Use of the cosine law. 


Example:
The side of the square that is inscribed into an equilateral triangle with the side length 6 is? 
Solution:
Given, a =
6.
x
=
? 









Geometry
and use of trigonometry contents  A 



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