## Pythagoras' Theorem Exercise

1. Name the hypotenuse in each of the following triangles?

 a. b. c. 2. Find the lengths of the sides (in cm) marked by letters (Give all answers correct to 3 significant figures):

 a. b. c. d. e. f. 3. State whether the following triangles are right-angled:

 (a) (b) (c) 4. Venito has a ladder which is 12.5 metres long.
She puts it up against the side wall of her house and the bottom of the ladder was 2.5 metres from the foot of the wall.
How far up the wall of the building would the ladder reach to the nearest centimetre?

5. A concrete slab is poured to form the base of a building.
The slab has a diagonal of 27 metres and the shortest side of the slab is 15 metres.
How long is the slab (to the nearest metre)?

 6. A builder wants to check that the framing for a door is perpendicular (at 90°). The door frame is 2.43 metres high, 1.62 metres wide and the diagonal of the frame is 2.92. Do you think the builder would be happy with his construction? 7. Two rugby posts are different heights.
The posts are 8 metres apart. A piece of string is placed from the top of one post to the top of the other. This string is measured at 865 cm long. How much higher is one post than the other?

8. A right cone has a radius of 3 cm and a height of 6 cm.
What is the slant height of the cone?

 9. A rectangular rugby field is twice as long as it is wide. Its perimeter is 390 m. Find the length of the diagonal, to the nearest metre.

10. Two roads cross at right angles.
Samantha and Seti leave the intersection at the same time in their cars.
Samantha drives her Subaru Impreza at an average speed of 70 km/h along one of the roads and Seti drives his Mitzubishi Magna down the other road at 75 km/h.
After half an hour, how far down each road have they driven and how far apart are they?