 4.01 Pythagoras' theorem

Worksheet
Pythagoras' theorem
1

For the following triangles, name the side that is the hypotenuse:

a
b
2

Determine whether the triangle shown is right-angled:

Unknown sides
3

Calculate the value of c in the following triangles, correct to two decimal places if necessary:

a
b
c
d
e
f
g
h
i
j
k
4

Calculate the value of a in the following triangles, correct to two decimal places if necessary:

a
b
c
d
e
f
5

Calculate the value of b in the following triangles, correct to two decimal places if necessary:

a
b
c
d
e
f
g
6

Find the length of the hypotenuse of a right-angled triangle, to two decimal places, given that the other two sides are:

a

7\text{ m} and 9\text{ m}

b

7\text{ mm} and 15\text{ mm}

c

13.6\text{ mm} and 1.2\text{ mm}

d

5\text{ mm} and 5\text{ mm}

e

14\text{ m} and 14\text{ m}

f

17.9\text{ m} and 17.9\text{ m}

7

Find the value of b, to two decimal places, where b is the length of one of the shorter sides of a right-angled triangle which has:

a
A hypotenuse of length 13\text{ mm} and another side of length 8\text{ mm}.
b
A hypotenuse of length 3\text{ cm} and another side of length 2\text{ cm}.
8

Consider the following figure. Complete the following, rounding your answers to two decimal places:

a

Find the value of x.

b

Find the value of y.

c

Hence, find the length of the base of the triangle.

9

Findt the value of the pronumeral in the following figures, correct to two decimal places:

a
b
c
d
10

Consider the following shape.

a

Find the value of x.

b

Find the value of y.

Applications
11

Iain’s car has run out of petrol. He walks 12 \text{ km} west and then 9 \text{ km} south looking for a petrol station.

If he is now h \text{ km} directly from his starting point, find the value of h.

12

The screen on a handheld device has dimensions 9\text{ cm} by 5\text{ cm}, and a diagonal of length x\text{ cm}. What is the value of x?

13

William and Kenneth are playing football together. At one point in the game, they are near the same corner of the field. William is on the goal line, 11 \text{ m} away from the corner, while Kenneth is on the side line, 17 \text{ m} away from the corner.

Find the shortest distance between William and Kenneth. Round your answer to two decimal places.

14

A soft drink can has a height of 11 \text{ cm} and a radius of 4 \text{ cm}. Find L, the length of the longest straw that can fit into the can.

Round your answer down to the nearest centimetre, to ensure it fits inside the can.

15

A movie director wants to shoot a scene where the hero of the film fires a grappling hook from the roof of one building to the roof of another. The shorter building is 37 \text{ m} tall, the taller building is 54 \text{ m} tall and the street between them is 10 \text{ m} wide.

Find the minimum length of rope, l, needed for the grappling hook. Give your answer correct to two decimal places.

16

A sports association wants to redesign the trophy they award to the player of the season. The front view of one particular design is shown below.

a

Find the value of x, correct to two decimal places.

b

Find the value of y, correct to two decimal places.

17

Fiona's house has the outer dimensions as shown in the diagram below:

Find the height of the house, h, to two decimal places.

18

Consider the crane shown:

To help bear heavier loads, a support cable joins the end of one arm of the crane to the other, through a small tower that rises h \text{ m} above the crane arm.

Find, to two decimal places:

a

The value of h.

b

The value of l.

c

The total length of the support cable.

19

A city council plans to build a seawall and boardwalk along a local coastline. According to safety regulations, the seawall needs to be 5.25 \text{ m} high and 7.66 \text{ m} deep and will be built at the bottom of a 14.78 \text{ m} long sloped section of shoreline. This means that the boardwalk will need to be built 2.43 \text{ m} above the seawall, so that it is level with the public area near the beach. This information is shown in the diagram below:

Find the width of the boardwalk, x \text{ m}, correct to two decimal places.