Find the length of the side for each pronumeral correct to two decimal places:
Find the angle for each pronumeral correct to two decimal places:
Use the sine rule to find the value of x, given that x is obtuse. Round your answer correct to two decimal places.
Point C has a bearing of 142 \degree from Point A. If Point B is 19 kilometres West of Point A, find the distance, x, between Point B and Point C. Round your answer to two decimal places.
Ellie is on a ski lift looking down to her two friends, Glen and Valentina, as they ski down the slope. Glen is 6 \text { m} away and at an angle of depression of 70 \degree, while Valentina is 9 \text { m} away, at an angle of depression of 45 \degree. Find the distance between Glen and Valentina, correct to one decimal place.
The Olsen family install a set of solar panels onto a flat section of their roof. The panels come as two identical parts, that fold out. Each part of these folding panels is s \text{ cm} long. The panels are held up by a triangular stand, the back part of which makes and angle of \theta with the roof.
Find the value of s, correct to two decimal places.
Hence find the value of \theta, correct to the nearest degree.
A blender has a set of blades at its base with measurements as shown in the diagram:
Find the angle \theta correct to the nearest minute.
Find the total area covered by the blades in the blender, correct to two decimal places.
Ellie and Tina set up their canvas tent, which is 213 \text{ cm} tall and 294 \text{ cm} wide. A pair of identical sheets on the front of the tent form an entrance between them. The inside length of these sheets is 235 \text{ cm}.
Find l, where l \text{ cm} is the slant height of the tent. Round your answer to two decimal places.
Find \theta correct to the nearest minute.
Find \alpha correct to the nearest minute.
Find the area covered by the sheets at the front of the tent, correct to two decimal places.
At a shopping mall, there is a vending machine located just under one of the escalators. The machine is 1.1 \text{ m} wide and 1.8 \text{ m} tall and is placed 3.9 \text{ m} away from the bottom of the escalator. The escalator goes up at an angle of \theta and the top of the escalator is at an angle of elevation of 70 \degree from the base of the vending machine.
Find the value of \theta, correct to the nearest minute.
Find d, where d \text{ m} is the distance between the bottom of the vending machine and the top of the escalator. Round your answer to two decimal places.
Find h, where h \text{ m} is the height of the escalator. Round your answer to two decimal places.
Lucy travelled on a bearing of 39 \degree from point A to point B. She then travelled on a bearing of 159 \degree for 17 \text{ km} to point C which is East of point A.
Find the value of x, the distance Lucy would have to travel due east to return to point A. Round your answer to two decimal places.
Hyatt's Ridge is a base camp for climbers of a mountain range. The nearby towns A, B and C are located around the edge of a small mountain, with roads connecting them around the mountainside. The government wants to build a tunnel through the mountain to connect towns A and B.
Find the angle \theta.
Find the length of the tunnel, b \text{ km}, between towns A and B. Round your answer to two decimal places.
Find the true bearing from town B to town A. Round your answer to the nearest degree.
Find the distance, t \text{ km}, between towns B and C. Round your answer to two decimal places.
Find the distance, d \text{ km}, between towns A and C. Round your answer to two decimal places.
Farmer Ted is looking to sell a portion of his property. The real estate agent asks him about the size and dimensions of his paddock, so he finds some old plans for the paddock's fences as shown. The dotted line represents a dividing fence that separates the two parts of the paddock.
Find the length of the dividing fence, correct to the nearest metre.
Find the missing side length of the paddock. Round your answer to the nearest metre.
Find the value of d. Round your answer to the nearest metre.
Find the total area of the paddock. Round your answer to the nearest square meter.
Yuri and his friends are on a bike ride from S to F, travelling directly at a compass bearing of N 54 \degree W. The entire trip is 96.27 \text{ km} long and they stop at R, which is one third of the way to F from S, and exactly 75.45 \text{ km} away from a mountain, M. Yuri doesn't know how far away the mountain was when he started or finished the ride, but he did notice that M was at a bearing of S 77 \degree W from S and S 9 \degree W from F.
Complete the diagram by marking it with all given information.
Find the compass bearing of M from R, to the nearest degree.
Find the distance SM, to two decimal places.
Find the distance FM, to two decimal places.
While writing a fantasy novel, Xanthe is designing the map of the locations in the novel. The main character must travel 34 \text{ km} on a bearing of 132 \degree T from Meydern to get to Arivode. He then sets out from Arivode and travels 26 \text{ km} on a bearing of 212 \degree T to get to Illduin.
Complete the diagram by marking it with all known information.
Find the distance between Illduin and Meydern, correct to the nearest kilometre.
Xanthe estimates that her main character's horse will travel at an average speed of 40 \text{ km} per hour. How long in total would it take for her character to visit all three of these towns, travelling by horse? Give your answer in hours, correct to one decimal place.
