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 = 13b = 15 and hc = 12.    AD = ?
 
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 = 3 , side b = 2 and angle a = 60, find angle b.
Solution:  Given,  a = 3 , b = 2 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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