Geometry - Triangle Problems and Solutions
      Triangle, solved problems, examples
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 = ?
 
Example:   Area of a triangle is 5 m2 the length of one side is 4 m and of other side 3 m, the sine of the angle between given sides is?
Solution:   Given,  A = 5 m2, a = 4 m  and  b = 3 m.  sin g = ?  
Example:   Sides of a triangle, a = 13, b = 14 and c = 15, find the radius of the circle center of which lies on the side c and which touches sides, a and b.
Solution:   Given,  a = 13, b = 14 and c = 15.  r = ?
 
Example:   To a circle of radius 30 cm, from a point distant 50 cm from the circle center, drown are both tangents. Find the distance between tangents.
Solution:   Given,  r = 30 cm and OS = 50 cm.   d(D1, D2) = d = ?
 
Example:   Angles of a triangle ABC, which lay at the side AB, are 70 and 80, if O is the intersection of altitudes of the triangle and d angle (AOB) then, the sind is?
Solution:   Given, a = 70 and b = 80.   sin d = ?
 
Example:   Around a square with the side a circumscribed is an equilateral triangle with the altitude h and the base coincident with the side of the square. Find the side of the equilateral triangle. 
Solution:   Given, a and  h.   x = ?
 
Example:   In a right triangle the bisector of the angle a divides opposite leg to two segments, find the ratio between greater and smaller of segments. 
Solution:   Given, a.   x / y = ?
 
Geometry and use of trigonometry contents - A
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