Measurement & Geometry · Guided Practice
Pythagoras Theorem
9 questions with answers and video solutions. Try each one before revealing the answer.
Calculate the length of the hypotenuse.
Answer
Calculate the length of the other shorter side.
Answer
Calculate the length of the hypotenuse.
Give your answer to 1 decimal place.
Answer
The foot of the ladder is m from the base of the wall.
Calculate how far up the wall the ladder reaches.
Give your answer to 1 decimal place.
Answer
Determine whether it is right-angled. Use your working to justify your answer.
Answer
The two are equal, so the triangle is right-angled.
Two cables support a section of the bridge. This section forms two right-angled triangles, as shown in the diagram.
(b) Calculate the total length of cable needed for this section of bridge. Do not use a scale drawing.
Answer
(b) 902.4... m
Jamel bought a stand for this fish tank.
The top of the stand is circular.
The corners of the square base of the tank touch the edge of the circle as shown.
The diameter of the circle is shown by the dotted line in the aerial view.
(c) Calculate the area of the top of the stand.
Give your answer in square metres.
Answer
0.141... m²
A boat sails due East from a harbour.
A lighthouse is 500 metres due North of the harbour.
When the boat is at position A it is 600 metres away from the lighthouse.
It sails a further 400 metres to position B.
Calculate the direct distance from position B to the lighthouse as shown by the dotted line.
Do not use a scale drawing.
Answer
Distance from harbour to A:
m
Distance from harbour to B = 331.66... + 400 = 731.66... m
Distance from lighthouse to B:
m
A badge has been designed in the shape of a right-angled triangle and a semi-circle.
The outside edge of the badge will be made of silver.
Calculate the length of silver needed for the outside edge of the badge.
Answer
31.99 cm