We read your photo as:

Calculate the distance BC.

March 20, 2026Mathematics

ScanSolve AI Answer

Answer

30\sqrt{111} m

8 steps

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).
Apply Pythagorean theorem.
$AC^{2} + BC^{2} = AB^{2}$
Substitute given values (include units).
$AC^{2} + (10\ \text{m})^{2} = (100\sqrt{10}\ \text{m})^{2}$
Calculate each term.
$AC^{2} + 100\ \text{m}^{2} = 10000 \times 10\ \text{m}^{2}$ $AC^{2} + 100\ \text{m}^{2} = 100000\ \text{m}^{2}$
Solve for $AC^{2}$ .
$AC^{2} = 100000\ \text{m}^{2} - 100\ \text{m}^{2}$ $AC^{2} = 99900\ \text{m}^{2}$
Take square root (include units).
$AC = \sqrt{99900}\ \text{m}$
Simplify $\sqrt{99900}$ .
$99900 = 100 \times 999 = 2^{2} \times 5^{2} \times 3^{3} \times 37 = 2^{2} \times 5^{2} \times 3^{2} \times (3 \times 37)$ $\sqrt{99900} = \sqrt{2^{2} \times 5^{2} \times 3^{2} \times 111} = 2 \times 5 \times 3 \times \sqrt{111} = 30\sqrt{111}$
Final answer (with units).
$AC = 30\sqrt{111}\ \text{m}$
30\sqrt{111} m

Was this helpful?

A new problem that tests the same skill.

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question