The screen on a handheld device has dimensions 9 \text{ cm} by 6 \text{ cm}, and a diagonal of length x \text{ cm}:
Find the value of x. Round your answer to two decimal places.
Sean’s car has run out of petrol. He walks 8 \text{ km} west and then 6 \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.
Find the value of k in the following figure. Round your answer to two decimal places.
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.
Yuri and Dave are playing football together. At one point in the game, they are near the same corner of the field. Yuri is on the goal line, 11 \text{ m} away from the corner, while Dave is on the side line, 17 \text{ m} away from the corner.
Find the shortest distance between Yuri and Dave. Round your answer to two decimal places.
A soft drink can has a height of 13 \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.
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.
The town Bunderidda is 3 \text{ km} directly south of Appleby and 4 \text{ km} directly west of Cottenham. Find the distance from Appleby to Cottenham.
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, rounded to two decimal places.
A ladder of height h \text{ cm} is placed against a vertical wall. If the bottom of the ladder is 80 \text{ cm} from the base of the wall and the top of the ladder touches the wall at a height of 150 \text{ cm}, find h.
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 given figure:
Find the value of x.
Find the value of y, correct to two decimal places.
Consider the following shape:
Find the value of d, rounded to one decimal place.
Tina's house has the outer dimensions as shown in the following diagram:
Find the height of the house, h, to two decimal places.
Two flagpoles of height 14 m and 19 m are 22 m apart. A length of string is connected to the tops of the two flagpoles and pulled taut.
Find the length of the string, to one decimal place.
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.
