Solve the Triangle a=100 , b=120 , c=85

Solve Math

Trigonometry

$a = 100$ , $b = 120$ , $c = 85$

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.

$A = \arccos (\frac{{(120)}^{2} + {(85)}^{2} - {(100)}^{2}}{2 (120) (85)})$

Simplify the results.

Tap for more steps...

Simplify the numerator.

Tap for more steps...

Raise $120$ to the power of $2$ .

$A = \arccos (\frac{14400 + {(85)}^{2} - {(100)}^{2}}{2 \cdot 120 \cdot 85})$

Raise $85$ to the power of $2$ .

$A = \arccos (\frac{14400 + 7225 - {(100)}^{2}}{2 \cdot 120 \cdot 85})$

Raise $100$ to the power of $2$ .

$A = \arccos (\frac{14400 + 7225 - 1 \cdot 10000}{2 \cdot 120 \cdot 85})$

Multiply $- 1$ by $10000$ .

$A = \arccos (\frac{14400 + 7225 - 10000}{2 \cdot 120 \cdot 85})$

Add $14400$ and $7225$ .

$A = \arccos (\frac{21625 - 10000}{2 \cdot 120 \cdot 85})$

Subtract $10000$ from $21625$ .

$A = \arccos (\frac{11625}{2 \cdot 120 \cdot 85})$

Simplify the denominator.

Tap for more steps...

Multiply $2$ by $120$ .

$A = \arccos (\frac{11625}{240 \cdot 85})$

Multiply $240$ by $85$ .

$A = \arccos (\frac{11625}{20400})$

Cancel the common factor of $11625$ and $20400$ .

Tap for more steps...

Factor $75$ out of $11625$ .

$A = \arccos (\frac{75 (155)}{20400})$

Cancel the common factors.

Tap for more steps...

Factor $75$ out of $20400$ .

$A = \arccos (\frac{75 \cdot 155}{75 \cdot 272})$

Cancel the common factor.

$A = \arccos (\frac{75 \cdot 155}{75 \cdot 272})$

Rewrite the expression.

$A = \arccos (\frac{155}{272})$

Evaluate $\arccos (\frac{155}{272})$ .

$A = 55.26002846$

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.

$B = \arccos (\frac{{(100)}^{2} + {(85)}^{2} - {(120)}^{2}}{2 (100) (85)})$

Simplify the results.

Tap for more steps...

Simplify the numerator.

Tap for more steps...

Raise $100$ to the power of $2$ .

$B = \arccos (\frac{10000 + {(85)}^{2} - {(120)}^{2}}{2 \cdot 100 \cdot 85})$

Raise $85$ to the power of $2$ .

$B = \arccos (\frac{10000 + 7225 - {(120)}^{2}}{2 \cdot 100 \cdot 85})$

Raise $120$ to the power of $2$ .

$B = \arccos (\frac{10000 + 7225 - 1 \cdot 14400}{2 \cdot 100 \cdot 85})$

Multiply $- 1$ by $14400$ .

$B = \arccos (\frac{10000 + 7225 - 14400}{2 \cdot 100 \cdot 85})$

Add $10000$ and $7225$ .

$B = \arccos (\frac{17225 - 14400}{2 \cdot 100 \cdot 85})$

Subtract $14400$ from $17225$ .

$B = \arccos (\frac{2825}{2 \cdot 100 \cdot 85})$

Simplify the denominator.

Tap for more steps...

Multiply $2$ by $100$ .

$B = \arccos (\frac{2825}{200 \cdot 85})$

Multiply $200$ by $85$ .

$B = \arccos (\frac{2825}{17000})$

Cancel the common factor of $2825$ and $17000$ .

Tap for more steps...

Factor $25$ out of $2825$ .

$B = \arccos (\frac{25 (113)}{17000})$

Cancel the common factors.

Tap for more steps...

Factor $25$ out of $17000$ .

$B = \arccos (\frac{25 \cdot 113}{25 \cdot 680})$

Cancel the common factor.

$B = \arccos (\frac{25 \cdot 113}{25 \cdot 680})$

Rewrite the expression.

$B = \arccos (\frac{113}{680})$

Evaluate $\arccos (\frac{113}{680})$ .

$B = 80.43441514$

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

$55.26002846 + C + 80.43441514 = 180$

Solve the equation for $C$ .

Tap for more steps...

Add $55.26002846$ and $80.43441514$ .

$C + 135.69444361 = 180$

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

Tap for more steps...

Subtract $135.69444361$ from both sides of the equation.

$C = 180 - 135.69444361$

Subtract $135.69444361$ from $180$ .

$C = 44.30555638$

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

$A = 55.26002846$

$B = 80.43441514$

$C = 44.30555638$

$a = 100$

$b = 120$

$c = 85$

Do you know how to Solve the Triangle a=100 , b=120 , c=85? 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	six hundred forty-eight million two hundred forty thousand four hundred twenty-five

Interesting facts

648240425 has 32 divisors, whose sum is 1080345600
The reverse of 648240425 is 524042846
Previous prime number is 79

Basic properties

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

Name

Name	six hundred seventy-four million eight hundred fourteen thousand eight hundred seventy-eight

Interesting facts

674814878 has 4 divisors, whose sum is 1012222320
The reverse of 674814878 is 878418476
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 53
Digital Root 8

Name

Name	one hundred twenty-one million six hundred eleven thousand two hundred ninety-nine

Interesting facts

121611299 has 4 divisors, whose sum is 121845240
The reverse of 121611299 is 992116121
Previous prime number is 521

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 32
Digital Root 5

Graph 500 degrees

Convert from Radians to Degrees -(17pi)/9

Factor f(x)=x^2+4x-32

Graph 9i+12j

Solve for x tan(x-(5pi)/4)=(-sin(x)+cos(x))/(-cos(x)-sin(x))