Consider the given triangle:
Find the value of \angle BAC.
Find the length of c. Round your answer to two decimal places.
Consider the following diagram:
Find the value of \angle OBA.
Find the length of k. Round your answer to two decimal places.
\triangle ABC consists of angles A, B and C which appear opposite sides a, b and c respectively. If the measures of a, c and A are given, which rule should be used to find the size of \angle C, the sine rule or the cosine rule?
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, to the nearest degree.
Hence, find the size of \angle SRQ, to the nearest degree.
A rhombus of side length 10 \text{ cm} has a longer diagonal of length 16 \text{ cm}.
Find the following, rounding your answers to one decimal place:
\theta, the obtuse angle.
x
d, the length of the shorter diagonal.
Consider the following diagram and given angle \angle DBC = 141\degree:
Find the following, rounding your answers to two decimal places:
y
x
r
d
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, 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 garden, in the shape of a quadrilateral, is represented in the given diagram:
Find the following, rounding your answers to two decimal places:
The length of BD.
The length of CD.
The perimeter of the garden.
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:
Each player is to sprint one lap and then jog one lap alternately, doing each 3 times.
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.
Two wires help support a tall pole. One wire forms an angle of 36 \degree with the ground and the other wire forms an angle of 70 \degree with 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 h, the height of the pole. 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 the size of \angle ABC, correct to two decimal places.
Find the size of \angle BCA, correct to two decimal places.
Find the distance from Dave to the building at B, correct to one decimal place.
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:
If the satellite is h \text{ km} above the ground, find h. Round your answer to two decimal places.
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 as shown in the diagram below:
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.
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 \degree, and from B the angle of depression is 47 \degree.
If the buildings are h \text{ m} tall, find the value of h. Round your answer to the nearest metre.
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.
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.
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.
To find the distance ST across a river, a distance VT = 137\text{ m} is measured on one side of the river. It is found that \angle SVT = 33 \degree 38 ' and \angle VTS = 119\degree. Find the distance ST to one decimal place.
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} to Point C, which is due East from point A.
Find the size of \angle BAC.
Find the size of \angle ABC.
Find the distance Neil is from his starting point. Round your answer to two decimal places.
Dave leaves town along a road on a bearing of 169 \degree and travels 26 \text{ km}. Maria leaves the same town on another road with a bearing of 289 \degree and travels 9 \text{ km}.
Calculate the distance between them to the nearest \text{km}.
Grenada \left(G\right), Tangiers \left(T\right) and Roma \left(R\right) are three towns. Grenada is on a bearing of 31 \degreefrom Tangiers and 312 \degreefrom Roma. Tangiers is due west of Roma. The distance from Grenada to Roma is 55 \text{ km}.
Find the distance from Grenada to Tangiers, x, to the nearest kilometre.
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.
A pod of dolphins following warm ocean currents were tracked travelling 10.3\text{ km} from Ryla to Luna on a bearing of 246 \degree, and then 8.1\text{ km} to Elara which is 14.9\text{ km} due south of Ryla.
Find the angle at which they changed direction when they got to Luna, to the nearest tenth of a degree.
Hence find the bearing of Elara from Luna.
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.
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}.
Find the distance covered by the meteoroid travelling towards point B in the 29 minutes after the collision.
Find the distance covered by the meteoroid travelling towards point C in the 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 angle of elevation to the top of a 44-metre high tower from point A, due west of the tower, is 52\degree. Point B is 200 metres away from point A on a bearing of 141\degree. Find the following, rounding your answers to two decimal places:
x, the distance from point A to the base of the tower.
y, the distance from point B to the base of the tower.
\theta, the angle of elevation from point B to the top of the tower.
Three radio towers are situated at points P, Q and R:
Towers P and Q are 41.1 \text{ km} apart, and the bearing of tower Q from P is 115 \degree.
The tower at R is due east of P and 28.4 km from Q.
According to this information, Tower R could have two different positions. Consider the following two cases and round your answers to one decimal place:
In the case where tower R is further from P:
Hence, find the bearing of R from Q.
In the case where tower R is closer P:
Hence, find the bearing of R from Q.