Shape and Space 4

In the right-angled triangle shown, one side is 12 cm long and the other side (adjacent to the right angle) is 5 cm long. Calculate the length of the hypotenuse.

State the sine ratio in a right-angled triangle in terms of the sides.

A right-angled triangle has a hypotenuse of 15 cm. One of the other sides is 9 cm. Work out the length of the remaining side.

Calculate the size of angle in a right-angled triangle where the side opposite is 7 m and the hypotenuse is 14 m. Give your answer correct to 3 significant figures.

PQRS is a rectangle. PQ = 6 cm and QR = 8 cm.

Explain why the diagonals of a rectangle are always equal in length.

A triangle has sides of length 3 cm, 4 cm, and 5 cm. Work out the area of the triangle.

A ladder 4.5 m long leans against a vertical wall, making an angle of 68° with the ground. Calculate the height above the ground that the top of the ladder reaches.

Triangle ABC is right-angled at B. AB = 6.2 cm and AC = 11.5 cm. Calculate, giving your answers to 3 significant figures,

A right-angled triangle has one angle of 55° and a hypotenuse of 9.3 cm. Find the length of the side adjacent to the 55° angle. Give your answer correct to 3 significant figures.