Name the hypotenuse of each triangle:
Use Pythagoras' theorem to determine whether the following triangles are right-angled:
Calculate the value of c in each of the following triangles, giving your answer correct to two decimal places where necessary:
Calculate the value of the pronumeral in each of the following triangles, giving your answer correct to two decimal places where necessary:
Find the value of the pronumeral in each of the triangles described, giving your answer correct to two decimal places where necessary:
c \text{ m} is the length of the hypotenuse of a right-angled triangle whose other two sides are 7 \text{ m} and 9 \text{ m} in length.
c \text{ mm} is the length of the hypotenuse of a right-angled triangle whose other two sides are 7 \text{ mm} and 15 \text{ mm} in length.
c \text{ mm} is the length of the hypotenuse of a right-angled triangle whose other two sides are 13.6 \text{ mm} and 1.2 \text{ mm} in length.
c \text{ mm }is the length of the hypotenuse of a right-angled triangle whose other two sides are each 5 \text{ mm} in length.
c \text{ m} is the length of the hypotenuse of a right-angled triangle whose other two sides are each 14 \text{ m} in length.
c \text{ m} is the length of the hypotenuse of a right-angled triangle whose other two sides are each 17.9 \text{ m} in length.
Find the value of the pronumeral in each of the triangles described, giving your answer correct to two decimal places where necessary:
b \text{ cm} is the length of one side of a right-angled triangle whose hypotenuse is 3 \text{ cm} in length and whose other side is 2 \text{ cm} in length.
b \text{ mm} is the length of one side of a right-angled triangle whose hypotenuse is 13 \text{ mm} in length and whose other side is 8 \text{ mm} in length.
Find the lengths of the unknown sides in each figure, giving your answers correct to two decimal places where necessary:
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 as shown in the diagram:
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 5 \text{ cm}, and a diagonal of length x \text{ cm}. Find the value of x, correct to two decimal places.
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.
Fiona's house has the outer dimensions as shown in the diagram below:
What is the height of the house, h? Round your answer 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 minimum length of rope, l, needed for the grappling hook. Give your answer correct 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 below:
Find the value of x, correct to two decimal places.
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.
What is the shortest distance between where Emma started and where she stopped for lunch?
What is the shortest distance between where Emma started and where she finished her journey? Round your answer 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.
What is the value of x?
What is the value of y?
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:
First find the value of x, correct to two decimal places.
Find the height of the pillar, h \text{ cm}, 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.