Solve the Triangle a=60 , b=67 , c=72

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Trigonometry

$a = 60$ , $b = 67$ , $c = 72$

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

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

Solve the equation.

$A = \arccos (\frac{b^{2} + c^{2} - a^{2}}{2 b c})$

Substitute the known values into the equation.

$A = \arccos (\frac{{(67)}^{2} + {(72)}^{2} - {(60)}^{2}}{2 (67) (72)})$

Simplify the results.

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Simplify the numerator.

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Raise $67$ to the power of $2$ .

$A = \arccos (\frac{4489 + {(72)}^{2} - {(60)}^{2}}{2 \cdot 67 \cdot 72})$

Raise $72$ to the power of $2$ .

$A = \arccos (\frac{4489 + 5184 - {(60)}^{2}}{2 \cdot 67 \cdot 72})$

Raise $60$ to the power of $2$ .

$A = \arccos (\frac{4489 + 5184 - 1 \cdot 3600}{2 \cdot 67 \cdot 72})$

Multiply $- 1$ by $3600$ .

$A = \arccos (\frac{4489 + 5184 - 3600}{2 \cdot 67 \cdot 72})$

Add $4489$ and $5184$ .

$A = \arccos (\frac{9673 - 3600}{2 \cdot 67 \cdot 72})$

Subtract $3600$ from $9673$ .

$A = \arccos (\frac{6073}{2 \cdot 67 \cdot 72})$

Simplify the denominator.

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Multiply $2$ by $67$ .

$A = \arccos (\frac{6073}{134 \cdot 72})$

Multiply $134$ by $72$ .

$A = \arccos (\frac{6073}{9648})$

Evaluate $\arccos (\frac{6073}{9648})$ .

$A = 50.98993634$

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.

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

Substitute the known values into the equation.

$B = \arccos (\frac{{(60)}^{2} + {(72)}^{2} - {(67)}^{2}}{2 (60) (72)})$

Simplify the results.

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Simplify the numerator.

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Raise $60$ to the power of $2$ .

$B = \arccos (\frac{3600 + {(72)}^{2} - {(67)}^{2}}{2 \cdot 60 \cdot 72})$

Raise $72$ to the power of $2$ .

$B = \arccos (\frac{3600 + 5184 - {(67)}^{2}}{2 \cdot 60 \cdot 72})$

Raise $67$ to the power of $2$ .

$B = \arccos (\frac{3600 + 5184 - 1 \cdot 4489}{2 \cdot 60 \cdot 72})$

Multiply $- 1$ by $4489$ .

$B = \arccos (\frac{3600 + 5184 - 4489}{2 \cdot 60 \cdot 72})$

Add $3600$ and $5184$ .

$B = \arccos (\frac{8784 - 4489}{2 \cdot 60 \cdot 72})$

Subtract $4489$ from $8784$ .

$B = \arccos (\frac{4295}{2 \cdot 60 \cdot 72})$

Simplify the denominator.

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Multiply $2$ by $60$ .

$B = \arccos (\frac{4295}{120 \cdot 72})$

Multiply $120$ by $72$ .

$B = \arccos (\frac{4295}{8640})$

Cancel the common factor of $4295$ and $8640$ .

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Factor $5$ out of $4295$ .

$B = \arccos (\frac{5 (859)}{8640})$

Cancel the common factors.

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Factor $5$ out of $8640$ .

$B = \arccos (\frac{5 \cdot 859}{5 \cdot 1728})$

Cancel the common factor.

$B = \arccos (\frac{5 \cdot 859}{5 \cdot 1728})$

Rewrite the expression.

$B = \arccos (\frac{859}{1728})$

Evaluate $\arccos (\frac{859}{1728})$ .

$B = 60.19124971$

The sum of all the angles in a triangle is $180$ degrees.

$50.98993634 + C + 60.19124971 = 180$

Solve the equation for $C$ .

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Add $50.98993634$ and $60.19124971$ .

$C + 111.18118606 = 180$

Move all terms not containing $C$ to the right side of the equation.

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Subtract $111.18118606$ from both sides of the equation.

$C = 180 - 111.18118606$

Subtract $111.18118606$ from $180$ .

$C = 68.81881393$

These are the results for all angles and sides for the given triangle.

$A = 50.98993634$

$B = 60.19124971$

$C = 68.81881393$

$a = 60$

$b = 67$

$c = 72$

Do you know how to Solve the Triangle a=60 , b=67 , c=72? 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 seven hundred forty-seven million four hundred thirty-one thousand three hundred ninety-five

Interesting facts

1747431395 has 16 divisors, whose sum is 2173482720
The reverse of 1747431395 is 5931347471
Previous prime number is 521

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 44
Digital Root 8

Name

Name	one billion two hundred ninety-four million five hundred eighty-six thousand six hundred seventy

Interesting facts

1294586670 has 64 divisors, whose sum is 3358200384
The reverse of 1294586670 is 0766854921
Previous prime number is 281

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 48
Digital Root 3

Name

Name	four million three hundred twenty-two thousand eight hundred five

Interesting facts

4322805 has 16 divisors, whose sum is 6990144
The reverse of 4322805 is 5082234
Previous prime number is 97

Basic properties

Is Prime? no
Number parity odd
Number length 7
Sum of Digits 24
Digital Root 6

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