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6.01 Pythagoras' theorem

Worksheet
Pythagoras' theorem
1

Consider the following right-angled triangle. Write the equation that can be constructed to find the value of x:

2

Determine whether the following are Pythagorean triples:

a

\left(6, 8, 13\right)

b

\left(5, 12, 13\right)

c

\left(2, 4, 6\right)

d

\left(3, 4, 5\right)

3

Find the length of the hypotenuse for the following triangles:

a
b
c
4

Find the length of the hypotenuse for the following triangles, give your answer as a surd:

a
b
c
d
e

The two smallest side lengths of a right-angled triangle are 6 and 9.

f

The two smallest side lengths of a right-angled triangle are 14 and 17.

g

The two smallest side lengths of a right-angled triangle are 6 and 7.

h

The two smallest side lengths of a right-angled triangle are 17 and 28.

5

Find the length of the unknown side for the following triangles:

a
b
c
d
6

Find the length of the unknown side for the following triangles, give your answers as a surd:

a
b
c
d
e

A right-angled triangle has a hypotenuse of length 9 and another side of length 3.

f

A right-angled triangle has a hypotenuse of length 17 and another side of length 14.

7

Find the base length of the following triangles:

a
b
Applications
8

The screen on a handheld device has dimensions 8\text{ cm} by 5 \text{ cm}, and a diagonal length of x cm. Find the value of x, round your answer to two decimal places.

9

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 m away from the corner, while Kenneth is on the side line, 17 m away from the corner.

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

10

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 m tall, the taller building is 54 m tall and the street between them is 10 m wide.

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

11

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 in the diagram:

a

Find the value of x.

b

Find the value of y.

12

Find the value of d in the following figure. Round your answer to one decimal place.

13

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

Find the height of the house, h, rounded to one decimal place.

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VCMMG346

Solve right-angled triangle problems including those involving direction and angles of elevation and depression.

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