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subject: Solve Three Sides [print this page]

Triangle has three sides each side have internal angles 'A', 'B' and 'C' and sides of length 'a', 'b' and 'c'.If we don't know the three values means we can find out that by using other three known values.This is known as solve three sides of triangle.We can use the formulas such as sum of angles, sine rule and cosine rule.

Formulas to Solve three Sides

1. The sum of the angles equals 180

A + B + C = 180

2. The 'sine rule:

a/sinA=b/sinB=c/sinC

3. The 'cosine rule' ...

a = b + c - 2bc cosA

or

b = a + c - 2ac cosB

or

c = b + a - 2ba cosC

The above rules are very important in problem solving.Solve three sides of triangles by given internal angles.

Example for How to Solve three Sides of Triangle with Known Values

The following steps are used to solve the problem:

Problem 1:

Step 1: Begin by using cosine rule to find the largest angle.

NOTE:First find largest internal angle.Next find second angle by using sine rule.Inverse sin operations give acute angles.We must eliminate the wrong answer.

The below example has largest angle 'C'.It will opposite to largest side.

Cosine rule:

c^2=b^2+a^2-2bacosC

cosC=(a^2+b^2-c^2)/2ab

=(1^2+2^2-2^2)/(2*1*2)

=0.25

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Find the inverse cos of 0.25:

C = cos-1(0.25)

= 75.52

Step 2: Find out the remaining angles by using sine rule.

The sine rule is easy to calculate.

To find angle:

a/sinA=c/sinC

sinA=asinC/c

=(2sin75.52)/4

=0.484117.

Find the inverse sin of 0.484117:

A = sin-1(0.484117)

= 28.954

Step 3: To find third angle.

By using sum of internal angles.

A + B + C = 180

so

B = 180 - (A+C)

= 180 - (28.954 + 75.52)

= 180 - 104.474

= 75.526

The Unknown angles are A=28.954,B=75.526 and C=75.52.

Problem 2:

In triangle ABC, angle A = 40 and angle b =40.Find angle c?

Solution:

The sum of the angles equals 180

So angle A + angle B + angle C = 180

40 + 40 + angle C = 180

80 + angle C = 180

angle C = 180 - 80

angle C = 100

by: nitinp

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