To use the cosine rule to find the length ofAC, which angle would need to be given?
Write the cosine rule for the given triangles as if to find side a:
For each of the following triangles, find the value of the pronumeral using the cosine rule. Round your answers to two decimal places.
In \triangle ABC, \cos C = \dfrac{8}{9}:
Find the exact length of side AB in centimetres.
In \triangle QUV, q = 5, u = 6 and \cos V = \dfrac{3}{5}. Find the value of v.
Find the length of the diagonal, x, in parallelogram ABCD:
Round your answer to two decimal places.
A parallelogram has a side of length 13 \text{ cm} and a diagonal of length 58 \text{ cm}:
If the angle between these two lengths is 17 \degreeand the length of the other side is x \text{ cm}, find the value of x. Round your answer to one decimal place.
Write an expression for \cos \theta using the cosine rule for the following triangle:
For each of the following triangles, find the value of the pronumeral in degrees. Round your answers to two decimal places.
Find the size of angle B using the cosine rule. Round your answer to the nearest second.
A triangle has sides of length 12\text{ cm}, 16\text{ cm} and 5\text{ cm}. Calculate the size of the largest angle in the triangle. Round your answer to the nearest minute.
The sides of a triangle are in the ratio 4:5:8. Find \theta, the smallest angle in the triangle. Round your answer to the nearest degree.
Consider the following parallelogram:
Calculate the size of \angle PSR. Round your answer to the nearest minute.
Hence, find \angle SRQ. Round your answer to the nearest minute.
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.
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.
The distance from her starting point to Point C is given by x\text{ km}. Find this distance to two decimal places.
Goal posts 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 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.
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, correct to one decimal place.
Hence, find the total length of the race, correct 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 \text{ min} after the collision?
What distance will the meteoroid travelling towards point C have covered 29 \text{ min} after the collision?
Find the distance between the two meteoroids 29 \text{ min} after the collision. Round your answer to the nearest tenth of a kilometre.
A teacher is writing exam questions for her maths class. She draws a triangle, labels the vertices A, B and C and labels the opposite sides a = 5, b = 8 and c = 15 respectively.
She wants to ask students to find the size of \angle A. Explain what the problem is with her question.
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.
In this question we will prove the cosine rule: a^{2} = b^{2} + c^{2} - 2 b c \cos A.
Find an expression for a^{2} in terms of c, x and h by using Pythagoras' theorem.
Find an expression for h^{2} by using Pythagoras' theorem in \triangle ACD.
Find an expression for x in terms of \cos A.
Substitute your expressions for h^2 and x into your expression for a^{2} to prove the cosine rule.
