Question

In a triangle abc, LC=90°, LA=45°, AB=5 √ 2, Find BC and AC. (using Pythagorean theorem to solve)​

Answer 1

The lengths of BC and AC in the right triangle ABC are both 5 units.

To find the lengths of BC and AC in a right triangle ABC, we can use the Pythagorean theorem. Given that angle LC = 90° and angle LA = 45°, we can determine that angle LB = 180° - 90° - 45° = 45° as well. This means that triangle ABC is an isosceles right triangle. We can use the Pythagorean theorem to find the lengths of BC and AC. Let's label BC as 'x' and AC as 'y'.

Using the Pythagorean theorem, we have:

x² + x² = (5√2)²

2x² = (5√2)²

2x² = 50

x² = 25

x = 5

So, BC = 5

Since triangle ABC is isosceles, AC = BC = 5

Therefore, BC = 5 units and AC = 5 units.