Solve the Triangle tri{4}{}{4}{}{2}{}

 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 4 \\ c = & 4 \\ a = & 2 \end{matrix} & \begin{matrix} A = \\ B = \\ C = \end{matrix} \end{matrix}$

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.

$A = \arccos (\frac{{(4)}^{2} + {(4)}^{2} - {(2)}^{2}}{2 (4) (4)})$

Simplify the results.

Tap for more steps...

Simplify the numerator.

Tap for more steps...

Raise $4$ to the power of $2$ .

$A = \arccos (\frac{16 + {(4)}^{2} - {(2)}^{2}}{2 \cdot 4 \cdot 4})$

Raise $4$ to the power of $2$ .

$A = \arccos (\frac{16 + 16 - {(2)}^{2}}{2 \cdot 4 \cdot 4})$

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

$A = \arccos (\frac{16 + 16 - 1 \cdot 4}{2 \cdot 4 \cdot 4})$

Multiply $- 1$ by $4$ .

$A = \arccos (\frac{16 + 16 - 4}{2 \cdot 4 \cdot 4})$

Add $16$ and $16$ .

$A = \arccos (\frac{32 - 4}{2 \cdot 4 \cdot 4})$

Subtract $4$ from $32$ .

$A = \arccos (\frac{28}{2 \cdot 4 \cdot 4})$

Simplify the denominator.

Tap for more steps...

Multiply $2$ by $4$ .

$A = \arccos (\frac{28}{8 \cdot 4})$

Multiply $8$ by $4$ .

$A = \arccos (\frac{28}{32})$

Cancel the common factor of $28$ and $32$ .

Tap for more steps...

Factor $4$ out of $28$ .

$A = \arccos (\frac{4 (7)}{32})$

Cancel the common factors.

Tap for more steps...

Factor $4$ out of $32$ .

$A = \arccos (\frac{4 \cdot 7}{4 \cdot 8})$

Cancel the common factor.

$A = \arccos (\frac{4 \cdot 7}{4 \cdot 8})$

Rewrite the expression.

$A = \arccos (\frac{7}{8})$

Evaluate $\arccos (\frac{7}{8})$ .

$A = 28.95502437$

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.

$B = \arccos (\frac{{(2)}^{2} + {(4)}^{2} - {(4)}^{2}}{2 (2) (4)})$

Simplify the results.

Tap for more steps...

Simplify the numerator.

Tap for more steps...

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

$B = \arccos (\frac{4 + {(4)}^{2} - {(4)}^{2}}{2 \cdot 2 \cdot 4})$

Raise $4$ to the power of $2$ .

$B = \arccos (\frac{4 + 16 - {(4)}^{2}}{2 \cdot 2 \cdot 4})$

Raise $4$ to the power of $2$ .

$B = \arccos (\frac{4 + 16 - 1 \cdot 16}{2 \cdot 2 \cdot 4})$

Multiply $- 1$ by $16$ .

$B = \arccos (\frac{4 + 16 - 16}{2 \cdot 2 \cdot 4})$

Add $4$ and $16$ .

$B = \arccos (\frac{20 - 16}{2 \cdot 2 \cdot 4})$

Subtract $16$ from $20$ .

$B = \arccos (\frac{4}{2 \cdot 2 \cdot 4})$

Simplify the denominator.

Tap for more steps...

Multiply $2$ by $2$ .

$B = \arccos (\frac{4}{4 \cdot 4})$

Multiply $4$ by $4$ .

$B = \arccos (\frac{4}{16})$

Cancel the common factor of $4$ and $16$ .

Tap for more steps...

Factor $4$ out of $4$ .

$B = \arccos (\frac{4 (1)}{16})$

Cancel the common factors.

Tap for more steps...

Factor $4$ out of $16$ .

$B = \arccos (\frac{4 \cdot 1}{4 \cdot 4})$

Cancel the common factor.

$B = \arccos (\frac{4 \cdot 1}{4 \cdot 4})$

Rewrite the expression.

$B = \arccos (\frac{1}{4})$

Evaluate $\arccos (\frac{1}{4})$ .

$B = 75.52248781$

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

$28.95502437 + C + 75.52248781 = 180$

Solve the equation for $C$ .

Tap for more steps...

Add $28.95502437$ and $75.52248781$ .

$C + 104.47751218 = 180$

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

Tap for more steps...

Subtract $104.47751218$ from both sides of the equation.

$C = 180 - 104.47751218$

Subtract $104.47751218$ from $180$ .

$C = 75.52248781$

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

$A = 28.95502437$

$B = 75.52248781$

$C = 75.52248781$

$a = 2$

$b = 4$

$c = 4$

Do you know how to Solve the Triangle tri{4}{}{4}{}{2}{}? 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.