Sec 2 Mathematics Pythagoras & Irrational Numbers topical questions

Find the hypotenuse of each right triangle with the given legs.

1. (a)Legs 3 and 4[1]
2. (b)Legs 9 and 12[1]
3. (c)Legs 7 and 24[1]

Find the missing leg of each right triangle.

1. (a)Hypotenuse 10, one leg 6[1]
2. (b)Hypotenuse 17, one leg 8[1]
3. (c)Hypotenuse 25, one leg 20[1]

Sort the numbers √3, 0.5, 4, 2/3.

1. (a)Which are irrational?[2]
2. (b)Which are rational?[1]

Find the hypotenuse of each right triangle with the given legs.

1. (a)Legs 8 and 15[1]
2. (b)Legs 20 and 21[1]

Find the missing leg of each right triangle.

1. (a)Hypotenuse 26, one leg 10[1]
2. (b)Hypotenuse 41, one leg 40[1]

Use the converse of Pythagoras’ theorem to test each triangle.

1. (a)Sides 9, 12, 15[2]
2. (b)Sides 5, 7, 9[2]

A kite flies on a 25 m string, held by a person standing at a point 20 m horizontally from the point directly below the kite.

1. (a)Identify the hypotenuse of the triangle in this story.[1]
2. (b)Find the kite’s height above the person’s hand level.[2]
3. (c)If the string were 30 m with the same 20 m horizontal distance, write the exact height as a surd.[1]

A television screen measures 40 inches wide and 30 inches high.

1. (a)Explain why the screen’s diagonal is the hypotenuse.[1]
2. (b)Find the diagonal of the screen.[1]
3. (c)A second screen is 48 inches wide and 20 inches high. Find its exact diagonal.[2]

Estimate each surd without a calculator.

1. (a)Between which two integers does √30 lie?[1]
2. (b)Between which two integers does √75 lie?[1]
3. (c)Which is larger: √50 or 7.1? Justify.[2]

Use the converse of Pythagoras’ theorem to test each triangle.

1. (a)Sides 10, 24, 26[2]
2. (b)Sides 12, 16, 25[1]

Two rectangular HDB corridor signs are checked. The first is 60 cm wide with a 100 cm diagonal; the second is 45 cm wide with a 75 cm diagonal.

1. (a)Find the height of the first sign.[2]
2. (b)Find the height of the second sign.[2]

A 6.5 m ladder leans against a wall with its base 2.5 m from the wall.

1. (a)How high up the wall does the ladder reach?[2]
2. (b)The base slides 1 m further from the wall. Find the new height, correct to 2 decimal places.[2]
3. (c)Did the top of the ladder rise or fall? Give a reason.[1]

A square field has a diagonal of 60 m.

1. (a)Write an exact equation for the side length s and solve it as a surd.[2]
2. (b)Estimate the side length to 1 decimal place.[2]
3. (c)State one reason for preferring the exact surd over the rounded value.[1]

A ship sails 30 km due east, then 40 km due north.

1. (a)How far is the ship from its starting point?[2]
2. (b)A second ship sails 45 km east and 60 km north. How far is it from its start?[1]
3. (c)Explain the pattern in your two answers.[2]

A staircase has 12 identical steps, each rising 18 cm and running 24 cm forward.

1. (a)Find the straight-line distance from the front edge of one step to the next.[1]
2. (b)Find the total height gained over the 12 steps.[1]
3. (c)Find the total horizontal run over the 12 steps.[1]
4. (d)Find the straight-line distance from the bottom of the staircase to the top.[2]