Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.

The perimeter of a triangle is the sum of its sides. Therefore, perimeter = a + b + c = 5 + 12 + 13 = 30.

The perimeter of a triangle is the sum of its sides: a + b + c = 8 + 15 + 17 = 40.

Using the cosine rule, cos A = (b² + c² - a²) / (2bc) = (15² + 17² - 8²) / (2 * 15 * 17) = 0.8.

Since the sides are in the ratio of a Pythagorean triplet (3, 4, 5), triangle ABC is a right triangle.

The sides satisfy the Pythagorean theorem, hence it is a right triangle.

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

Angle O = 180 - (angle M + angle N) = 180 - (45 + 45) = 90 degrees.

Using Heron's formula, s = (10 + 24 + 26)/2 = 30. Area = √(30(30-10)(30-24)(30-26)) = √(30*20*6*4) = 120 cm².

Since 8^2 + 15^2 = 17^2, triangle XYZ is a right triangle.

Rearranging gives sin(x) = -√3/2, so x = 4π/3 and x = 5π/3.

The solution is x = π/2.

Rearranging gives cos^2(x) = 1/3, so x = π/3 and 2π/3.

The solution is x = π/3.

The only solution is x = π/2.

The solutions are x = 2π/3 and x = 4π/3 in the interval [0, 2π].

The solutions are x = 0, π, 2π.

The equation sin(2x) = 1 gives 2x = π/2 + 2nπ, hence x = π/4 + nπ/2. In [0, 2π], the solutions are π/4 and 5π/4.

The solutions are x = π/12, 5π/12, 7π/12, and 11π/12.

The solutions are x = 0, π, 2π, and x = nπ/3 for n = 0, 1, 2, 3, 4, 5.

The solutions are x = π/6 and x = 5π/6 in the interval [0, 2π].

The solutions are x = π/3 and x = 4π/3 in the interval [0, 2π].

The solutions are x = π/3 and x = 4π/3.

The solutions are x = π/3 and x = 4π/3.

Area = 1/2 * base * height => 24 = 1/2 * 8 * height => height = 6 cm.

Area = 1/2 * base * height => 30 = 1/2 * 10 * height => height = 6 units.

Since 7^2 + 24^2 = 25^2, triangle ABC is a right triangle.

The only solution is x = 0.

The solutions are x = 2π/3 and 4π/3.

The solutions are x = 2π/3 and x = 4π/3.