Sine Law Examples

The trigonometric sine law formula is used to calculate the unknown side of the triangle. In triangle we recognize the either sides or angle we can calculate the sizes of the other sides and angles. If we can consider the right triangle, we can make use of simple trigonometric ratios to determine the unidentified lengths of the side of the triangle.  Within a general triangle, you need using other technique; they are the laws of sines and cosines formulas. Let us see about the sine law examples.

Sine Law Examples

 

Consider the following triangle

 In the figure denotes the triangle.

In the above triangle include the inside angles A, B and C. 

Trigonometry law of sines

If any three values are recognized then we can obtain the other three values.

Total of the inside angles of the triangle equivalent to 180º

A+B+C = 1800

We can find the sides of triangle using sine rule.

`a/sinA = b/sin B = c/sin C`

Examples for Sine Law

 

Example 1 for sine law 

 

Compute the unknown side of the triangle.

In the figure has the side b = 37.

Solution

The total of the internal angles equal to one eighty degree

 A + B + C = 180º

Therefore

        C = 180º - (A+B) 

           = 180º - (30º+70º)

           = 180º - 100º

       C = 80º

To compute side c using the sine rule

`b/sinB = c/sinC`

`c = (37 sin 80^0)/sin 70^0`

   = 37 x 1.0480

c = 38.776

To compute side a using the sine rule

`a/sinA = b/sin B`

`a = (37 sin 30^0)/sin 70^0 `

   = 37 x 0.5320

a = 19.684

Thus the sides of the given triangle a = 19.684 and c = 38.776

 

Example 2 for sine law

 

Compute the unknown side of the triangle.

In the figure has the side b = 43

Solution

The total of the internal angles equal to one eighty degree

 A + B + C = 180º

Therefore

        C = 180º - (A+B) 

           = 180º - (30º+70º)

           = 180º - 100º

       C = 80º

To compute side c using the sine rule

`b/sinB = c/sinC`

`c = (43 sin 80^0)/sin 70^0`

   = 43 x 1.0480

c = 45.064

To compute side a using the sine rule

`a/sinA = b/sin B`

`a = (43 sin 30^0)/sin 70^0 `

   = 43 x 0.5320

a = 22.876

Thus the sides of the given triangle a = 22.876 and c = 45.064

These are the examples for sine law.