In mathematics, the triangles are nothing but the shapes which is made by 3 lines in topic geometry. In geometry, the sides are used to calculate the angles in triangles. The classification of triangles is named as Equilateral triangle, scalene triangle, Isosceles triangle, Right triangle, obtuse triangle, and acute triangle. The formula to calculate the angles in triangles are given below.
Calculate Angles in a Triangle – Formulas:
In geometry, there are different types of formulas to calculate the values of angles in the triangles. To calculate the angles value of right angle triangles we are having certain formulas based on the sides. Let as consider x, y and z are the three sides of the right angle triangles and X is the angles of the right angle triangles. Then Pythagoras theorem is used to calculate the value of angles in right triangles.
The Right Angle Triangles are shown below:
Formulas to calculate the angles of the right triangles are given as,
Sin A = x/z
cos A = y/z
Tan A = x/y
Formula to calculate the sides of the right triangles is given as,
x2 + y2 = z2
Calculate Angles in a Triangle – Examples:
Example 1: Calculate the angles A using the given data x = 5 and y = 8?
Sol:
From the given data x = 5 and y = 8
The diagram is given as,
Formula to calculate the sides of the right triangles is given as,
x2 + y2 = z2
52 + 82 = z2
25 + 64 = z2
z2 = 89
z = 9.4
Formulas to calculate the angles of the right triangles are given as,
Sin A = x/z
Sin A = 5/9.4
Sin A = .53
A = Sin-1 (.53)
A = 32.13
Example 2: Calculate the angles A using the given data x= 8 and z = 14?
Sol:
From the given data x= 8 and z = 14
The diagram is given as,
Formulas to calculate the angles of the right triangles are given as,
Sin A = x/z
Sin A = 8/14
Sin A = .57
A = Sin-1 (.57)
A = 34.84
Calculate angles in a triangle - Practice problem:
Problem 1: Calculate the angles A using the given data x= 6 and y = 17?
Answer is given below:
z = 18.02
A = 19.26
Problem 2:Calculate the angles A using the given data x= 5 and z = 14.6?
Answer is given below:
A = 11.86
Calculate Angles in a Triangle – Formulas:
In geometry, there are different types of formulas to calculate the values of angles in the triangles. To calculate the angles value of right angle triangles we are having certain formulas based on the sides. Let as consider x, y and z are the three sides of the right angle triangles and X is the angles of the right angle triangles. Then Pythagoras theorem is used to calculate the value of angles in right triangles.
The Right Angle Triangles are shown below:
Formulas to calculate the angles of the right triangles are given as,
Sin A = x/z
cos A = y/z
Tan A = x/y
Formula to calculate the sides of the right triangles is given as,
x2 + y2 = z2
Calculate Angles in a Triangle – Examples:
Example 1: Calculate the angles A using the given data x = 5 and y = 8?
Sol:
From the given data x = 5 and y = 8
The diagram is given as,
Formula to calculate the sides of the right triangles is given as,
x2 + y2 = z2
52 + 82 = z2
25 + 64 = z2
z2 = 89
z = 9.4
Formulas to calculate the angles of the right triangles are given as,
Sin A = x/z
Sin A = 5/9.4
Sin A = .53
A = Sin-1 (.53)
A = 32.13
Example 2: Calculate the angles A using the given data x= 8 and z = 14?
Sol:
From the given data x= 8 and z = 14
The diagram is given as,
Formulas to calculate the angles of the right triangles are given as,
Sin A = x/z
Sin A = 8/14
Sin A = .57
A = Sin-1 (.57)
A = 34.84
Calculate angles in a triangle - Practice problem:
Problem 1: Calculate the angles A using the given data x= 6 and y = 17?
Answer is given below:
z = 18.02
A = 19.26
Problem 2:Calculate the angles A using the given data x= 5 and z = 14.6?
Answer is given below:
A = 11.86
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