Question 1: A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. Calculate the length of the other shorter side using the formula a² = c² - b².

Answer: 12

Question 2: In a right triangle, the hypotenuse is 17 m, and one shorter side is 8 m. Find the other shorter side.

Answer: 15

Question 3: Calculate the shorter side of a right-angled triangle if the hypotenuse is 10 units and the other side is 6 units.

Answer: 8

Question 4: A ladder leans against a wall, forming a right triangle with the ground. If the hypotenuse is 15 m and the distance from the wall to the base of the ladder is 9 m, find the height of the ladder above the ground.

Answer: 12

Question 5: A square-based pyramid has a slant height of 10 cm and a half-length of the base of 6 cm. Calculate the vertical height of the pyramid.

Answer: 8

Question 6: A triangle has a hypotenuse of 25 cm. If one shorter side is 24 cm, verify the length of the other side using the formula a² = c² - b².

Answer: 7

Question 7: Identify the mistake in the following calculation: a = √(c² - b²) with c = 10 and b = 8, resulting in a = 19.

Answer: Incorrect calculation; √(100 - 64) = 8, not 19

Question 8: Construct a right-angled triangle such that the hypotenuse is 20 units and one short side is 12 units. Use the grid to draw and verify the length of the remaining side.

Answer: 16

Question 9: A corridor is 24 meters long, and a camera is mounted at the ceiling at one end. If the camera's line of sight includes a point 7 meters from the far end of the corridor, find the height of the ceiling assuming right-angled triangle formation.

Answer: 17

Question 10: A rectangular garden has a diagonal of 12 meters, and one side measures 5 meters. Find the length of the other side.

Answer: 11

Question 11: Explain why the formula a² = c² - b² only applies to right-angled triangles when finding the shorter side.

Answer: Because it is derived from the Pythagorean theorem, which applies only to right-angled triangles.