Shape and measurement ʚɞ

Which of the following statements about Pythagoras' theorem is correct?

a) Pythagoras' theorem relates the angles of a triangle to the lengths of its sides.

b).

c) T

d)

• Pythagoras' theorem relates the angles of a triangle to the lengths of its sides.

• In a right-angled triangle, the side opposite the right angle is called the hypotenuse, which is always the shortest side.

• The hypotenuse is always the longest side of a right-angled triangle.

• Pythagoras' theorem only applies to equilateral triangles.

The sum of the areas of the squares of the two shorter sides (a and b) equals the area of the square of the hypotenuse.

Write down the equation:

Using Pythagoras’ theorem to calculate the length of the hypotenuse:

Calculate the length of the hypotenuse in the triangle opposite, correct to two decimal places.

Using Pythagoras’ theorem to calculate the length of an unknown side in a right-angled triangle:

Calculate the length of the unknown side, x, in the triangle opposite. Give the answer correct to one decimal place.

Using Pythagoras’ theorem to solve a practical problem:

A helicopter hovers at a height of 150 m above the ground and is a horizontal distance of 220 m from a landing pad. Find the direct distance of the helicopter from the landing pad, correct to two decimal places.

Pythagoras' theorem:

• Find the length of side 𝑐c in a right-angled triangle with sides 4.2 cm and 2.5 cm

Applying Pythagoras' theorem in real-life scenarios:

• A ladder rests against a brick wall. The base of the ladder is 1.5 m from the wall, and the top reaches 3.5 m up the wall. Find the length of the ladder, correct to one decimal place

1. Finding distances and lengths using Pythagoras' theorem:

   • A rectangular block of land measures 28 m by 55 m. John wants to put a fence along the diagonal. How long will the fence be? Give the answer correct to three decimal places.

Using Pythagoras’ theorem in three dimensions:

The cube in the diagram has sides of length 5 cm. Find these lengths correct to two decimal places: a AC b AD

Using Pythagoras’ theorem in three-dimensional problems:

For the square pyramid shown in the diagram, calculate: a the length AC, correct to two decimal places b the height EF, correct to one decimal place.