Topic Review — Pythagoras’ Theorem

Review Questions

1. Finding the hypotenuse. Fluency

   1. Legs 9 cm and 12 cm. Find the hypotenuse.
   2. Legs 5 m and 12 m. Find the hypotenuse.
   3. Legs 8 cm and 15 cm. Find the hypotenuse.
   4. Legs 7 cm and 24 cm. Find the hypotenuse.
   5. Legs 6 m and 8 m. Find the hypotenuse.

2. Finding a shorter side. Fluency

   1. Hypotenuse = 13 cm, one leg = 5 cm. Find the other leg.
   2. Hypotenuse = 25 m, one leg = 20 m. Find the other leg.
   3. Hypotenuse = 17 cm, one leg = 15 cm. Find the other leg.
   4. Hypotenuse = 10 m, one leg = √19 m. Find the other leg.
   5. Hypotenuse = 29 cm, one leg = 20 cm. Find the other leg. Round to 2 d.p. if necessary.

3. Converse of Pythagoras’ theorem. Fluency

   1. Is a triangle with sides 10, 24, 26 right-angled? Show working.
   2. Is a triangle with sides 6, 9, 12 right-angled? Show working.
   3. Is a triangle with sides 15, 36, 39 right-angled? Show working.
   4. A triangle has sides 7, 7, and 10. Is it right-angled? If not, is it acute or obtuse?

4. Mixed applications. Understanding

   1. A rectangular block of wood is 12 cm long, 5 cm wide, and 4 cm tall. Find the length of the space diagonal.
   2. Find the distance between A(−2, 1) and B(4, 9) on a coordinate plane. Leave as an exact value.
   3. An isosceles triangle has a base of 16 cm and equal sides of 17 cm. Find the height of the triangle.
   4. A cable runs from the top of a 24 m pole to a peg in the ground 10 m from the base. Find the exact length of the cable.
   5. A right triangle has a hypotenuse of 2√10 cm and one leg of 2 cm. Find the exact length of the other leg.

5. Problem solving. Problem Solving

   1. A builders’ plan shows a right-angled triangular section of a roof. The two legs are 3.6 m and 4.8 m. Find the length of the rafter (hypotenuse) and the area of the triangular section.
   2. A helicopter flies 40 km due east and then 30 km due south. How far is it, in a straight line, from its starting point? It then needs to return directly to the start. If it travels at 120 km/h, how many minutes does the return trip take?
   3. A right-angled triangle has legs in the ratio 3 : 4. The hypotenuse is 20 cm. Find the lengths of the two legs.
      1. Set up an equation using the ratio and Pythagoras’ theorem.
      2. Solve to find the two leg lengths.
      3. Verify by checking the Pythagorean triple.
   4. The screen of a laptop is described as “15-inch diagonal”. Its aspect ratio is 16:9 (width:height).
      1. Using the ratio and Pythagoras’ theorem, find the exact width and height of the screen.
      2. Calculate the area of the screen to 1 d.p.