Solve the Triangle a=8 , c=7 , B=31.8

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Trigonometry

$a = 8$ , $c = 7$ , $B = 31.8$

Use the law of cosines to find the unknown side of the triangle, given the other two sides and the included angle.

$b^{2} = a^{2} + c^{2} - 2 a c \cos (B)$

Solve the equation.

$b = \sqrt{a^{2} + c^{2} - 2 a c \cos (B)}$

Substitute the known values into the equation.

$b = \sqrt{{(8)}^{2} + {(7)}^{2} - 2 \cdot 8 \cdot 7 \cos (31.8)}$

Simplify the results.

Tap for more steps...

Raise $8$ to the power of $2$ .

$b = \sqrt{64 + {(7)}^{2} - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Raise $7$ to the power of $2$ .

$b = \sqrt{64 + 49 - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Multiply $- 2$ by $8$ .

$b = \sqrt{64 + 49 - 16 \cdot (7 \cos (31.8))}$

Multiply $- 16$ by $7$ .

$b = \sqrt{64 + 49 - 112 \cos (31.8)}$

Add $64$ and $49$ .

$b = \sqrt{113 - 112 \cos (31.8)}$

Use the law of cosines to find the unknown side of the triangle, given the other two sides and the included angle.

$b^{2} = a^{2} + c^{2} - 2 a c \cos (B)$

Solve the equation.

$b = \sqrt{a^{2} + c^{2} - 2 a c \cos (B)}$

Substitute the known values into the equation.

$b = \sqrt{{(8)}^{2} + {(7)}^{2} - 2 \cdot 8 \cdot 7 \cos (31.8)}$

Simplify the results.

Tap for more steps...

Raise $8$ to the power of $2$ .

$b = \sqrt{64 + {(7)}^{2} - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Raise $7$ to the power of $2$ .

$b = \sqrt{64 + 49 - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Multiply $- 2$ by $8$ .

$b = \sqrt{64 + 49 - 16 \cdot (7 \cos (31.8))}$

Multiply $- 16$ by $7$ .

$b = \sqrt{64 + 49 - 112 \cos (31.8)}$

Add $64$ and $49$ .

$b = \sqrt{113 - 112 \cos (31.8)}$

Use the law of cosines to find the unknown side of the triangle, given the other two sides and the included angle.

$b^{2} = a^{2} + c^{2} - 2 a c \cos (B)$

Solve the equation.

$b = \sqrt{a^{2} + c^{2} - 2 a c \cos (B)}$

Substitute the known values into the equation.

$b = \sqrt{{(8)}^{2} + {(7)}^{2} - 2 \cdot 8 \cdot 7 \cos (31.8)}$

Simplify the results.

Tap for more steps...

Raise $8$ to the power of $2$ .

$b = \sqrt{64 + {(7)}^{2} - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Raise $7$ to the power of $2$ .

$b = \sqrt{64 + 49 - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Multiply $- 2$ by $8$ .

$b = \sqrt{64 + 49 - 16 \cdot (7 \cos (31.8))}$

Multiply $- 16$ by $7$ .

$b = \sqrt{64 + 49 - 112 \cos (31.8)}$

Add $64$ and $49$ .

$b = \sqrt{113 - 112 \cos (31.8)}$

Use the law of cosines to find the unknown side of the triangle, given the other two sides and the included angle.

$b^{2} = a^{2} + c^{2} - 2 a c \cos (B)$

Solve the equation.

$b = \sqrt{a^{2} + c^{2} - 2 a c \cos (B)}$

Substitute the known values into the equation.

$b = \sqrt{{(8)}^{2} + {(7)}^{2} - 2 \cdot 8 \cdot 7 \cos (31.8)}$

Simplify the results.

Tap for more steps...

Raise $8$ to the power of $2$ .

$b = \sqrt{64 + {(7)}^{2} - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Raise $7$ to the power of $2$ .

$b = \sqrt{64 + 49 - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Multiply $- 2$ by $8$ .

$b = \sqrt{64 + 49 - 16 \cdot (7 \cos (31.8))}$

Multiply $- 16$ by $7$ .

$b = \sqrt{64 + 49 - 112 \cos (31.8)}$

Add $64$ and $49$ .

$b = \sqrt{113 - 112 \cos (31.8)}$

Use the law of cosines to find the unknown side of the triangle, given the other two sides and the included angle.

$b^{2} = a^{2} + c^{2} - 2 a c \cos (B)$

Solve the equation.

$b = \sqrt{a^{2} + c^{2} - 2 a c \cos (B)}$

Substitute the known values into the equation.

$b = \sqrt{{(8)}^{2} + {(7)}^{2} - 2 \cdot 8 \cdot 7 \cos (31.8)}$

Simplify the results.

Tap for more steps...

Raise $8$ to the power of $2$ .

$b = \sqrt{64 + {(7)}^{2} - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Raise $7$ to the power of $2$ .

$b = \sqrt{64 + 49 - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Multiply $- 2$ by $8$ .

$b = \sqrt{64 + 49 - 16 \cdot (7 \cos (31.8))}$

Multiply $- 16$ by $7$ .

$b = \sqrt{64 + 49 - 112 \cos (31.8)}$

Add $64$ and $49$ .

$b = \sqrt{113 - 112 \cos (31.8)}$

Use the law of cosines to find the unknown side of the triangle, given the other two sides and the included angle.

$b^{2} = a^{2} + c^{2} - 2 a c \cos (B)$

Solve the equation.

$b = \sqrt{a^{2} + c^{2} - 2 a c \cos (B)}$

Substitute the known values into the equation.

$b = \sqrt{{(8)}^{2} + {(7)}^{2} - 2 \cdot 8 \cdot 7 \cos (31.8)}$

Simplify the results.

Tap for more steps...

Raise $8$ to the power of $2$ .

$b = \sqrt{64 + {(7)}^{2} - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Raise $7$ to the power of $2$ .

$b = \sqrt{64 + 49 - 2 \cdot 8 \cdot (7 \cos (31.8))}$

Multiply $- 2$ by $8$ .

$b = \sqrt{64 + 49 - 16 \cdot (7 \cos (31.8))}$

Multiply $- 16$ by $7$ .

$b = \sqrt{64 + 49 - 112 \cos (31.8)}$

Add $64$ and $49$ .

$b = \sqrt{113 - 112 \cos (31.8)}$

There are not enough parameters given to solve the triangle.

Unknown triangle

Do you know how to Solve the Triangle a=8 , c=7 , B=31.8? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	one billion two hundred fifty-three million forty-nine thousand seven hundred seventy-three

Interesting facts

1253049773 has 8 divisors, whose sum is 1257287808
The reverse of 1253049773 is 3779403521
Previous prime number is 1777

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 41
Digital Root 5

Name

Name	seven hundred ninety-six million eight hundred eighty-eight thousand eight hundred four

Interesting facts

796888804 has 32 divisors, whose sum is 1998393120
The reverse of 796888804 is 408888697
Previous prime number is 19

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 58
Digital Root 4

Name

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

Interesting facts

1996874531 has 4 divisors, whose sum is 1997359512
The reverse of 1996874531 is 1354786991
Previous prime number is 4153

Basic properties

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

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