# Solve the Triangle tri{15}{}{}{}{9}{106}

Solve the Triangle tri{15}{}{}{}{9}{106}
Use the law of cosines to find the unknown side of the triangle, given the other two sides and the included angle.
Solve the equation.
Substitute the known values into the equation.
Simplify the results.
Raise to the power of .
Raise to the power of .
Multiply by .
Multiply by .
Evaluate .
Multiply by .
Evaluate the root.
The law of sines is based on the proportionality of sides and angles in triangles. The law states that for the angles of a non-right triangle, each angle of the triangle has the same ratio of angle measure to sine value.
Substitute the known values into the law of sines to find .
Solve the equation for .
Multiply both sides of the equation by .
Simplify both sides of the equation.
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify the right side.
Simplify .
Evaluate .
Divide by .
Multiply by .
Take the inverse sine of both sides of the equation to extract from inside the sine.
Simplify the right side.
Evaluate .
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Subtract from .
The solution to the equation .
Exclude the invalid angle.
The sum of all the angles in a triangle is degrees.
Solve the equation for .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
These are the results for all angles and sides for the given triangle.
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### Name

Name one billion five hundred seventy-four million six hundred sixty-nine thousand five hundred ninety-one

### Interesting facts

• 1574669591 has 8 divisors, whose sum is 1612970064
• The reverse of 1574669591 is 1959664751
• Previous prime number is 53

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 53
• Digital Root 8

### Name

Name one billion seven hundred million seven hundred sixty-six thousand seven hundred fifty-eight

### Interesting facts

• 1700766758 has 16 divisors, whose sum is 2581804800
• The reverse of 1700766758 is 8576670071
• Previous prime number is 149

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 47
• Digital Root 2

### Name

Name eight hundred twenty-one million three hundred eighty thousand four hundred ninety

### Interesting facts

• 821380490 has 8 divisors, whose sum is 1267272864
• The reverse of 821380490 is 094083128
• Previous prime number is 35

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 35
• Digital Root 8