Calculate the distance BC.

March 20, 2026Mathematics

ScanSolve AI Answer

March 20, 2026

Answer

$30\sqrt{111} m$

Step 1: Identify the right triangle ABC with right angle at C.
Given:
$BC = 10$ m (one leg),
$AB = 100\sqrt{10}$ m (hypotenuse).
Find $CA$ (other leg).

Step 2: Apply Pythagorean theorem.

AC^{2} + BC^{2} = AB^{2}

Step 3: Substitute given values (include units).

AC^{2} + (10\ m)^{2} = (100\sqrt{10}\ m)^{2}

Step 4: Calculate each term.

AC^{2} + 100\ m^{2} = 10000 \times 10\ m^{2}

AC^{2} + 100\ m^{2} = 100000\ m^{2}

Step 5: Solve for $AC^{2}$ .

AC^{2} = 100000\ m^{2} - 100\ m^{2}

AC^{2} = 99900\ m^{2}

Step 6: Take square root (include units).

AC = \sqrt{99900}\ m

Step 7: Simplify $\sqrt{99900}$ .

99900 = 100 \times 999 = 2^{2} \times 5^{2} \times 3^{3} \times 37 = 2^{2} \times 5^{2} \times 3^{2} \times (3 \times 37)

\sqrt{99900} = \sqrt{2^{2} \times 5^{2} \times 3^{2} \times 111} = 2 \times 5 \times 3 \times \sqrt{111} = 30\sqrt{111}

Step 8: Final answer (with units).

AC = 30\sqrt{111}\ m

30\sqrt{111 m}

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Quick Answer

Identify the right triangle ABC with right angle at C. Given: BC = 10 m (one leg), AB = 100sqrt(10) m (hypotenuse).

Asked on March 20, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 20, 2026

Step 1: Identify the right triangle ABC with right angle at C. Given: BC = 10 m (one leg), AB = 100sqrt(10) m (hypotenuse). Find CA (other leg). Step 2: Apply Pythagorean theorem. AC^2 + BC^2 = AB^2 Step 3: Substitute given values (include units). AC^2 + (10\ m)^2 = (100sqrt(10)\ m)^2 Step 4: Calculate each term. AC^2 + 100\ m^2 = 10000 × 10\ m^2 AC^2 + 100\ m^2 = 100000\ m^2 Step 5: Solve for AC^2. AC^2 = 100000\ m^2 - 100\ m^2 AC^2 = 99900\ m^2 Step 6: Take square root (include units). AC = sqrt(99900)\ m Step 7: Simplify sqrt(99900). 99900 = 100 × 999 = 2^2 × 5^2 × 3^3 × 37 = 2^2 × 5^2 × 3^2 × (3 × 37) sqrt(99900) = sqrt(2^2) × 5^2 × 3^2 × 111 = 2 × 5 × 3 × sqrt(111) = 30sqrt(111) Step 8: Final answer (with units). AC = 30sqrt(111)\ m 30sqrt(111) m