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Geometry
- Triangle Problems and Solutions |
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Triangle, solved problems, examples |
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Example:
Lengths of sides of a triangle are in the proportion 9
: 10 : 17, find the radius of the incircle if the
difference of the
longest and the shortest side is 16
cm. |
Solution:
Given,
a
: b : c = 9 : 10 : 17 and
c
-
a = 16
cm.
r = ? |
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Example:
The side AB
of a triangle ABC
is 9
cm long. Sides, AC
and BC, form on a line
l, which is
parallel to side AB, the
segment 3
cm long. If the distance of the vertex C from the line
l is
3
cm, find the distance of the line l from the
side AB. |
Solution:
As shown triangles
are similar following proportion must hold, |
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9 : 3 = (3 + x) : 3 |
3
· (3 + x) = 3 · 9 |
3 + x = 9 |
x = 6 cm. |
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Example:
One leg and the hypotenuse of a right triangle are in relation 3
: 5, the perimeter of the triangle is
16 cm, find the area of the
triangle. |
Solution:
Given, a
: c = 3 : 5 and
P =
36
cm.
A = ? |
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Example:
In a circle of radius R
inscribed is a right triangle whose area is 96
and the sum of legs 28
cm, find
the radius R. |
Solution:
Given, A =
96
cm2 and
a
+ b = 28 cm.
R = ? |
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Example:
In a right triangle with hypotenuse c
= 10
cm inscribed
is a circle of radius r
= 2 cm,
area of the triangle
is? |
Solution:
Given, c =
10 cm
and r =
2 cm.
AD
=
? |
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Example:
If the ratio between angles in a triangle
a
: g
= 1/6 : 1/8
and b
: g
= 1/3 : 1/2
then, the smallest angle in the
triangle is? |
Solution: Given,
a
: g
= 1/6 : 1/8 and
b
: g
= 1/3 : 1/2.
a,
b and
g
=
? |
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Geometry
and use of trigonometry contents - A |
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