Consider the following triangle:
Name the hypotenuse.
Write Pythagoras' theorem for this triangle.
Is a + b > c?
Name the hypotenuse in each triangle:
Find the value of c in the following triangles, correct to two decimal places where necessary:
Find the length of the hypotenuse of a right-angled triangle, to two decimal places, given that the other two sides are:
7 \text{ m} and 9 \text{ m} in length
7 \text{ mm} and 15 \text{ mm} in length
Both 17.9 \text{ m} in length
Calculate the value of b in the following triangles. Round your answers to two decimal places where necessary.
Calculate the value of a in the following triangles. Round your answers to two decimal places where necessary.
Find the length of the unknown side, b, in the following right-angled triangles, rounding your answers to two decimal places:
A triangle whose hypotenuse is 3 \text{ cm} in length and whose other side is 2 \text{ cm} in length.
A triangle whose hypotenuse is 13 \text{ mm} in length and whose other side is 8 \text{ mm} in length.
Consider the following figure. Complete the following, rounding your answers to two decimal places:
Find the value of x.
Find the value of y.
Hence, find the length of the base of the triangle.
Consider the following shapes.
Find the value of x, correct to two decimal places if necessary.
Find the value of y, correct to two decimal places if necessary.
Find the value of the pronumeral for the following trapeziums. Round your answers to two decimal places.
Consider the following trapezium:
Find the value of a.
Find the value of b.
Find the value of x. Round your answer to two decimal places.
Find the perimeter of the trapezium. Round your answer to two decimal places.
Consider the following shape:
Find the value of x.
Find the value of y.
Find the value of z.
For each of the following triangles:
Write Pythagoras' theorem for the triangle.
Determine whether the side lengths satisfy Pythagoras' theorem.
Determine whether the triangles is a right-angled triangle.
Determine whether each of the following sets of three lengths could represent the sides of a right-angled triangle:
4, 3, 2
4, 3, 5
6, 8, 10
5, 12, 13
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.
The screen on a handheld device has dimensions 9 \text{ cm} by 6 \text{ cm}, and a diagonal of length x \text{ cm}.
What is the value of x?
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.
Consider the cone with slant height of 13 m and perpendicular height of 12 m:
Find the length of the radius, r.
Hence, find the length of the diameter of the cone's base.
A soft drink can has a height of 11 cm and a radius of 4 cm. Find L, the length of the longest straw that can fit into the can.
Round your answer down to the nearest cm, to ensure it fits inside the can.
The top of a flag pole is 4 \text{ m} above the ground and the shadow cast by the flag pole is 9 \text{ m} long. Find the distance from the top of the flag pole to the end of its shadow, correct to two decimal places.
Fiona's house has the outer dimensions as shown in the diagram below:
Find the height of the house, h, to two decimal places.
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 difference in height between the shorter building the the taller building.
Find the minimum length of rope, l, needed for the grappling hook. Round your answer to two decimal places.
Consider the crane shown in the diagram. 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 m above the crane arm.
Find, to two decimal places:
The value of h
The value of l
The total length of the support cable
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:
Find the value of x.
Find the value of y, correct to two decimal places.
Emma hikes south of her starting position for 834 \text{ m} and then 691 \text{ m} east, before stopping for a lunch break. She then travels south again for 427 \text{ m} before arriving at her final destination.
Find the shortest distance between where Emma started and where she stopped for lunch, correct to two decimal places.
Find the shortest distance between where Emma started and where she finished her journey, correct to two decimal places.
A farmer wants to build a fence around the entire perimeter of his land, as shown in the diagram. The fencing costs \$37 per metre.
Find the length of \text{GE}.
Find the value of x, to two decimal places.
Find the length of \text{BD}.
Find the value of y, to two decimal places.
Find the perimeter of the land. Round your answer to two decimal places.
How many metres of fencing does the farmer require, if fencing is sold by the metre?
At \$37 per metre of fencing, how much will it cost him to build the fence along the entire perimeter of the land?
Archeologists have uncovered an ancient pillar which, after extensive digging, remains embedded in the ground. The lead researcher wants to record all of the dimensions of the pillar, including its height above the ground.
However, the team can only take certain measurements accurately without risking damage to the artifact. These measurements are shown in the diagram.
Find the value of x, correct to two decimal places.
Hence, find h, the height of the pillar, correct to two decimal places.
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 m high and 7.66 m deep and will be built at the bottom of a 14.78 m long sloped section of shoreline. This means that the boardwalk will need to be built 2.43 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 m, correct to two decimal places.
A group of engineering students have made a triangle out of some wooden strips. They have made a triangle with sides lengths 20 \text{ m}, 48 \text{ m}, and 52 \text{ m}.
Show that the triangle they made is a right-angled triangle.
How many metres of wooden strips did they use to make the triangle?
Find the side lengths of other right-angled triangles they could create using the exact same length of wooden strips.