Pythagoras' Theorem and Right-Angled Triangle Trigonometry — Questions

IGCSE Mathematics (0580) practice questions. Work through each question before checking the solutions page.

Question 1

[2](a)A right-angled triangle has two shorter sides of 3 cm and 4 cm. Calculate the hypotenuse.

Question 2

[2](a)In a right-angled triangle, the opposite side to an angle is 5 cm and the hypotenuse is 8 cm. Calculate the angle.

Question 3

[2](a)A ladder leans against a wall. Its foot is 3.5 m from the wall, and the top reaches 2.0 m up the wall. Calculate the angle of elevation the ladder makes with the ground.

Question 4

[2](a)A right-angled triangle has legs 5 cm and 12 cm. Calculate the hypotenuse.

Question 5

[2](a)A right-angled triangle has hypotenuse 13 cm and one other side 5 cm. Calculate the third side.

Question 6

[2](a)In a right-angled triangle, the adjacent side is 6 cm and the hypotenuse is 10 cm. Calculate the angle between them.

Question 7

[2](a)A tree casts observation angle of elevation 25° from a point 50 m away on level ground. Calculate the height of the tree.

Question 8

[2](a)A right-angled triangle has hypotenuse 10 cm and one angle of 40°. Calculate the length of the side opposite this angle.

Question 9

[2](a)Using the same triangle, calculate the side adjacent to the 40° angle.

Question 10

[2](a)A person stands 200 m from the base of a tower and observes the top at an angle of elevation matching an angle of depression from the top of 100 m height. Calculate this angle.

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