In a 45-45-90 triangle, the legs are equal and each leg = hypotenuse/√2 = 10/√2 = 5√2 cm.

In a right triangle, the sum of the angles is 180 degrees. Therefore, the other angle must also be 45 degrees.

In a 45-45-90 triangle, the legs are equal, so the ratio is 1:1.

In a 45-45-90 triangle, the sides opposite the 45-degree angles are equal, hence the ratio is 1:1.

In a 45°-45°-90° triangle, the sides opposite and adjacent are equal, so the ratio is 1:1.

In a right triangle, the angle opposite the shortest side is the smallest angle, which is 30 degrees.

Using the Pythagorean theorem, a² + b² = c², we have 3² + b² = 5², which gives b² = 25 - 9 = 16, hence b = 4 cm.

Using Pythagorean theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

Using the Pythagorean theorem, a² + b² = c², we have 3² + b² = 5², which gives b² = 25 - 9 = 16, so b = 4 units.

Using the Pythagorean theorem, c = √(3² + 4²) = √(9 + 16) = √25 = 5 units.

Using Pythagorean theorem: hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.

Using the Pythagorean theorem: c = sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10.

Using the Pythagorean theorem, a² + b² = c², we have 6² + b² = 10². Thus, 36 + b² = 100, leading to b² = 64, so b = 8 cm.

Area = 1/2 * leg1 * leg2 = 1/2 * 6 * 8 = 24 cm².

Using the Pythagorean theorem: hypotenuse = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 cm.

Using the Pythagorean theorem: a² + b² = c². Here, 8² + b² = 10². Thus, 64 + b² = 100, so b² = 36, and b = 6 cm.

Using Pythagorean theorem: hypotenuse = √(9² + 12²) = √(81 + 144) = √225 = 15 cm.

Using the Pythagorean theorem, hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.

Using the Pythagorean theorem, c² = a² + b². Here, c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 cm.

Using the Pythagorean theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

sin(θ) = opposite/hypotenuse = 3/5

Mean = (22 + 25 + 25 + 30 + 35) / 5 = 107 / 5 = 26.4.

The mode is 2 and 4, but since we need one answer, we can choose 2 as it appears first.

Corresponding angles are equal, so angle 5 is also 60 degrees.

Same-side interior angles are supplementary, so 180 - 150 = 30 degrees.

Corresponding angles are equal, so the corresponding angle also measures 120 degrees.

Corresponding angles are equal, so the opposite angle also measures 75 degrees.

Corresponding angles are equal, so the opposite angle also measures 85 degrees.

Adjacent angles are supplementary, so the adjacent angle measures 180° - 110° = 70°.

Vertically opposite angles are equal. Therefore, the vertically opposite angle also measures 30 degrees.