Solve for H H = square root of K^2+(L-C)^2

$H = \sqrt{K^{2} + {(L - C)}^{2}}$

Step 1

Rewrite ${(L - C)}^{2}$ as $(L - C) (L - C)$ .

$H = \sqrt{K^{2} + (L - C) (L - C)}$

Step 2

Expand $(L - C) (L - C)$ using the FOIL Method.

Apply the distributive property.

$H = \sqrt{K^{2} + L (L - C) - C (L - C)}$

Apply the distributive property.

$H = \sqrt{K^{2} + L \cdot L + L (- C) - C (L - C)}$

Apply the distributive property.

$H = \sqrt{K^{2} + L \cdot L + L (- C) - C L - C (- C)}$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $L$ by $L$ .

$H = \sqrt{K^{2} + L^{2} + L (- C) - C L - C (- C)}$

Rewrite using the commutative property of multiplication.

$H = \sqrt{K^{2} + L^{2} - L C - C L - C (- C)}$

Rewrite using the commutative property of multiplication.

$H = \sqrt{K^{2} + L^{2} - L C - C L - 1 \cdot - 1 C \cdot C}$

Multiply $C$ by $C$ by adding the exponents.

Move $C$ .

$H = \sqrt{K^{2} + L^{2} - L C - C L - 1 \cdot - 1 (C \cdot C)}$

Multiply $C$ by $C$ .

$H = \sqrt{K^{2} + L^{2} - L C - C L - 1 \cdot - 1 C^{2}}$

Multiply $- 1$ by $- 1$ .

$H = \sqrt{K^{2} + L^{2} - L C - C L + 1 C^{2}}$

Multiply $C^{2}$ by $1$ .

$H = \sqrt{K^{2} + L^{2} - L C - C L + C^{2}}$

Subtract $C L$ from $- L C$ .

Move $L$ .

$H = \sqrt{K^{2} + L^{2} - C L - C L + C^{2}}$

Subtract $C L$ from $- C L$ .

$H = \sqrt{K^{2} + L^{2} - 2 C L + C^{2}}$