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

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Name

Name	one billion one hundred seventy-four million four hundred thirty-nine thousand one hundred forty-three

Interesting facts

1174439143 has 4 divisors, whose sum is 1175005048
The reverse of 1174439143 is 3419344711
Previous prime number is 2083

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 37
Digital Root 1

Name

Name	one billion ninety-two million two hundred sixty-two thousand three hundred fifty

Interesting facts

1092262350 has 32 divisors, whose sum is 2145927168
The reverse of 1092262350 is 0532622901
Previous prime number is 43

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 30
Digital Root 3

Name

Name	one billion five hundred thirty-four million four hundred twenty-four thousand five hundred thirty-nine

Interesting facts

1534424539 has 8 divisors, whose sum is 1680708960
The reverse of 1534424539 is 9354244351
Previous prime number is 29

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 40
Digital Root 4

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