A triangle has sides of length 13 \text{ cm}, 15 \text{ cm} and 5 \text{ cm}. The largest angle has a size of x . Calculate x. Round your answer to the nearest degree.
Find the length of the diagonal, x, in parallelogram ABCD.
Round your answer to two decimal places.
Consider the parallelogram in the given diagram that has a side of length 13 \text{ cm} and a diagonal of length 58 \text{ cm}:
Find the value of x. Round your answer to one decimal place.
Consider the given parallelogram:
Find the value of x\degree, to the nearest degree.
Hence, find the size of \angle SRQ, to the nearest degree.
Mae went for a bike ride on Sunday morning from Point A to Point B, which was 18 \text{ km} long. She then took a 126 \degree turn and rode from Point B to Point C, which was 21 \text{ km} long.
Find x, the distance in kilometres from her starting point to Point C to two decimal places.
A goal has posts that are 2 \text{ m} apart. Buzz shoots for the goal when he is 2.6 \text{ m} from one post and 3.1 \text{ m} from the other post.
Find the size of the angle, x\degree, in which he can score a goal. Round your answer to the nearest degree.
A pendulum of length 82 \text{ cm} swings a horizontal distance of 31 \text{ cm}.
Find the angle x of the pendulum's movement. Round your answer to the nearest degree.
A rhombus of side length 10 \text{ cm} has a longer diagonal of length 16 \text{ cm}.
Find \theta, the obtuse angle in the rhombus, to one decimal place.
Find x, shown in the diagram, to one decimal place.
Hence, calculate d, the length of the shorter diagonal of the rhombus, to one decimal place.
Point C has a bearing of 142 \degree from Point A. If Point B is 19 \text{ km} West of Point A, determine the distance, x, between Point B and Point C.
A garden, in the shape of a quadrilateral, is represented in the following diagram:
Find the following, rounding your answers to two decimal places:
The length of BD.
The length of CD.
The perimeter of the garden.
In a sailing boat race, teams must start at buoy A and navigate around buoys B and C before returning to buoy A to cross the line. The first leg of the race is 170.2 \text{ km} long, the second leg of the race is 150.9 \text{ km} long, and the angle between these legs is 111 \degree.
Find x, the distance of the third leg of the race. Round your answer to one decimal place.
Hence, find the total length of the race. Round your answer to one decimal place.
After two meteoroids collide at point A, one starts travelling in the direction of point B, while the other starts travelling in the direction of point C, with an angle of 53 \degree between the two directions. The meteoroid projected in the direction of B is moving at a speed of 7860 \text{ km/h}, while the other is moving at a speed of 10\,170 \text{ km/h}.
What distance will the meteoroid travelling towards point B have covered 29 minutes after the collision?
What distance will the meteoroid travelling towards point C have covered 29 minutes after the collision?
Find the distance between the two meteoroids 29 minutes after the collision. Round your answer to the nearest tenth of a kilometre.
The ball is kicked out of bounds in a soccer match and Pascal's team gets to throw the ball back onto the field. When the ball is thrown, Pascal is 12.6 \text{ m} away from Eraviste and the angle between him, Eraviste and the path of the ball is 56 \degree. The ball will hit the ground 13.1 \text{ m} away from Eraviste.
Find the distance, y \text{ m} , that Pascal needs to cover to reach the ball when it hits the field. Round your answer to one decimal place.
If it takes 1.6 seconds for the ball to hit the field after it is thrown, how fast will Pascal have to run to receive the ball in time? Round your answer in metres per second, to one decimal place.
Three fishing spots are shown in the diagram below:
Find the size of the angle \theta to the nearest degree.
Similarly, find the other two angles in the triangle formed at Sharpton and Wavemeet.
Hence find the compass bearing from Troutberk to each of the other fishing spots.
Lucy is a videographer and has recently bought a drone to capture aerial footage. She wants to test how fast the drone can fly and so flies the drone in a straight line directly above her. According to the readings on the remote control, the drone starts 2.8 \text{ m} away from Lucy and after 1.3 seconds, it is 4.6 \text{ m} away. The angle difference between where the done started and finished is 118 \degree.
Find the distance covered by the drone, to two decimal places.
Find the average speed of the drone in meters per second, to two decimal places.
Dave leaves a town along a road on a bearing of 166 \degree and travels 28 \text{ km}. Christa leaves the same town on another road with a bearing of 272 \degree and travels 7 \text{ km}. Find the distance between Dave and Christa, x \text{ km}, to the nearest kilometre.
A pod of dolphins following warm ocean currents were tracked travelling 5.8 \text{ km} from Ryla to Luna on a bearing of 224 \degree, and then 10.7 \text{ km} to Elara which is 12.8 \text{ km} due south of Ryla.
Find \theta, the angle at which they changed direction when they got to Luna. Round your answer to the nearest minute.
Hence find the bearing of Elara from Luna, to the nearest minute.
Edward uses a regular pentagon with sides of 8 \text{ cm} each to draw a five pointed star by drawing straight lines between each of the pentagon’s vertices. He then erases the dashed lines.
Find \theta, the angle between two of the star's points.
Hence, find the length of one of the star’s sides. Round your answer to two decimal places.
Peter drops an expensive photo frame. When he examines the frame, he notices that there are several cracks running in straight lines across the glass. He makes the diagram shown so that he can find out how much it will cost to fix, where the dashed lines represent the cracks:
Find the value of x, giving your answer correct to one decimal place.
Find the value of k, giving your answer correct to one decimal place.
If the cost to fix the cracks is \$0.85 for each centimetre of damage, how much will Peter need to pay?
In a game of pool, a player has one last ball to sink into a corner pocket. The player must use his cue (stick) to hit the white ball so that it knocks the purple ball into the corner pocket.
The player judges that the white ball is about 1.5 \text{ m} away from the corner pocket, and that the distance between the two balls is about 0.9 \text{ m}, while the purple ball is also 0.9 \text{ m} from the corner pocket.
He wants to find the angle \theta at which he needs to knock the white ball against the purple ball. Round your answer to two decimal places.
On the last day of a hike, students need to travel from their campsite, C, to the nearby train station, T. There is a path going directly east by train, but they instead decide to visit a couple of landmarks on their way so their teacher draws a map of the route:
Find the true bearing from the campsite, C, to the waterfall, W, correct to the nearest degree.
Find the true bearing from the waterfall to the rest stop, R, correct to the nearest degree.
Find the direct distance, d \text{ m}, between the rest stop and the train station. Round your answer to the nearest metre.
If the students hiked directly east from camp to the train station without seeing any landmarks, how far would they have traveled?
If the students walk at an average speed of 0.8 metres per second, find how much longer it would take to visit all the landmarks on the way to the station, compared to only walking directly to the train station from the campsite. Round your answer to the nearest minute.