A radio signal is sent from a transmitter at tower T, via a satellite S, to a town W, as shown in the diagram. The town is 526 \text{ km} from the transmitter tower. The signal is sent out from the transmitter tower at an angle of 18 \degree, and the town receives the signal at an angle of 26 \degree.
Find the size of \angle WST.
Find the distance, SW, that the signal travels from the satellite to the town. Round your answer to the nearest kilometre.
If the satellite is h \text{ km} above the ground, find h. Round your answer to two decimal places.
While in squash practise, Jack tries a kind of shot called a 'boast', where he hits the ball against the side wall so that it hits the front wall soon afterwards.
The ball travels 2.34 m from his racquet to the side wall, bouncing off it at an angle of 83 \degree. It then travels a further 2.12 m to hit the front wall.
Find the value of d correct to two decimal places, where d m is the distance from Jack's racquet to the point that the ball hits the front wall.
To calculate the height of each block of flats, a surveyor measures the angles of depression from A and B to C. From A, the angle of depression is 31 \degreeand from B the angle of depression is 47 \degree.
Find the size of \angle ACB.
If the distance between A and C is b \text{ m}, find the value of b. Round your answer to two decimal places.
If the buildings are h \text{ m} tall, find the value of h. Round your answer to the nearest metre.
Judy and Xavier need to build a bridge over a river, along the line ST. In order to find out how long the bridge needs to be, Judy stays at point T and measures the angle at T to point S to be 112 \degree while Xavier walks for 355 m down the river to point V where the angle to point S is 28 \degree 51 '. If the length of the bridge they will build is d \text{ m} , find d correct to one decimal place.
During football training, the coach marks out the perimeter of a triangular course that players need to run around. The diagram shows some measurements taken of the course, where side length a = 14 \text{ m}:
Find \angle A.
Find the length of side c. Round your answer to two decimal places.
Find the length of side b. Round your answer to two decimal places.
Each player must sprint one lap around the triangle and then jog one lap around the triangle. This process is to be done 3 times by each player.
If Tara can run 280 \text{ m/min}, and can jog at half the speed she runs, how long will this exercise take her? Round your answer to one decimal place.
Consider the following diagram:
Find \angle OBA.
Find the value of k. Round your answer to two decimal places.
Dave is standing on a hill and can see two buildings in the distance. Suppose the buildings are 20 \text{ km} apart. Dave is 13 \text{ km} from one building and the angle between the two lines of sight to the buildings is 35 \degree.
Find \angle ABC. Round your answer to two decimal places.
Find \angle BCA. Round your answer to two decimal places.
Find the distance from Dave to the building at B. Round your answer to one decimal place.
A bridge connects two towns on either side of a gorge, where one side of the gorge is inclined at 59 \degree and the other side is inclined at 70 \degree. The length of the steeper incline is 59.1 \text{ m}.
Find x, the length of the bridge. Round your answer correct to one decimal place.
Mae observes a tower at an angle of elevation of 12 \degree. The tower is perpendicular to the ground. Walking 67 \text{ m} towards the tower, she finds that the angle of elevation increases to 35 \degree:
Calculate the angle \angle ADB.
Find the length of the side a. Round your answer to two decimal places.
Find the height, h, of the tower. Round your answer to one decimal place.
Grenada \left(G\right), Tangiers \left(T\right) and Roma \left(R\right) are three towns. Grenada bears 15\degree from Tangiers and 319 \degree from Roma. Tangiers is due west of Roma. The distance from Grenada to Roma is 53 \text{ km}.
Find the distance from Grenada to Tangiers, x, to the nearest kilometre.
Two wires help support a tall pole. One wire forms an angle of 36 \degreewith the ground and the other wire forms an angle of 70 \degreewith the ground. The wires are 29 \text{ m} apart:
Find a, the angle made between the two wires at the top of the pole.
Find d, the length of the longest wire in metres. Round your answer to two decimal places.
Find calculate h, the height of the pole in metres. Round your answer to two decimal places.
Neil travelled on a bearing of 26 \degree from Point A to Point B. He then travelled on a bearing of 121 \degree for 18 \text{ km} towards Point C, which is sue East from point A.
Find the size of \angle BAC.
Find the size of \angle ABC.
Determine how far Neil is from his starting point, A. Round your answer correct to two decimal places.
Competitors taking part in a fundraising event must make their way around a triangular course set up in open water. They must swim from buoy A to buoy B, stand-up paddle from buoy B to buoy C, and a kayak from buoy C back to buoy A.
The buoys are set up such that \angle CAB = 61 \degree 17 ' and \angle ABC = 73 \degree 12 '. The swimming leg is 250 \text{ m} long.
Find BC, the length of the stand-up paddling leg of the course, correct to the nearest tenth of a metre.
Find AC, the length of the kayaking leg of the course, correct to the nearest tenth of a metre.
If the maximum time possible to finish the course is 22 minutes, find the slowest possible average speed of a competitor throughout the course. Round your answer to one decimal place.
An astronomy research group uses three different satellite dishes to analyse radiation from objects in outer space. The research group needs to know the exact locations of each dish with respect to another, with only the following information on their positions:
Starting at dish A, dish B is 91.4 km away at a bearing of S 35 \degree Wand dish C is at a bearing of S 16 \degree E. Dishes B and C are 102.8 km apart.
Complete the diagram by marking it with all known information.
Find the value of \theta, correct to the nearest minute.
Find the value of z, correct to two decimal places.
A team arrives at the airport in Tikaani for a month-long conservation expedition and are driven at a bearing of 149 \degree \text{T} for 342 \text{ km} until they arrive at a remote location, Kapik. They then begin a hike through the jungle, travelling at a bearing of 54 \degree \text{T} for to get to ancient ruins at Suluk. The group return from Suluk to Tikaani directly by travelling at a bearing of 278 \degree \text{T}.
Find f, where f \text{ km} is the distance between Kapik and Suluk. Round your answer to two decimal places.
Find d, where d \text{ km} is the distance between Suluk and Tikaani. Round your answer to two decimal places.
John and Patricia are playing hide and seek and Patricia decides to hide on top of the treehouse in their backyard. She spots John on the ground at an angle of depression of 47 \degree. The treehouse itself is 1.8 \text{ m} tall and John is 4.3 \text{ m} away from the base of the treehouse.
Find the value of \alpha, correct to the nearest degree.
Hence, find the value of \theta correct to the nearest degree.
If John is 17 metres tall, find how far Patricia is from the ground correct to one decimal place.
Two harbor patrol boats meet at point P before they check the entrance to the harbor. One boat goes to the headland at point Q, while the other boat goes to the another headland at point R. They then meet again on the other sides of the headlands at point S.
The crew of the first boat recorded that they first traveled 3419 \text{ m} at a bearing of 032^\circ \text{T} to point S and then traveled at a bearing of 112 \degree \text{T} to get to S. The second boat's crew recorded that they first traveled at a bearing of 049^\circ \text{T} and then at a bearing of 081^\circ \text{T}.
Find the value of the following, correct to the nearest metre:
