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Cosine rule - MYP Questionbank | RevisionDojo

Practice Cosine rule with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

A student attempts to find an angle $A$ in a triangle with side lengths $a = 20, b = 10,$ and $c = 8$ . Their calculator returns a 'domain error'. What is the most likely mathematical reason for this?

Question 2

A triangle has side lengths of $8$ , $11$ , and $15$ . Calculate the measure of the smallest angle in the triangle to one decimal place.

Question 3

A triangle has side lengths $a=4$ , $b=5$ , and $c=8$ . If you calculate $\cos C$ using the cosine rule, what does the resulting value indicate about angle $C$ ?

Question 4

To find the smallest angle in a triangle with side lengths $8, 15,$ and $17$ , which of the following fractions would be input into the inverse cosine function?

Question 5

For a triangle with side lengths $x$ , $y$ , and $z$ , let the angle opposite side $y$ be $Y$ . If $\cos Y < 0$ , which of the following mathematical relationships must be true?

Question 6

In triangle $PQR$ , you are given side lengths $p = 15\text{ cm}$ , $r = 22\text{ cm}$ , and the included angle $\angle Q = 75^{\circ}$ . Which expression correctly calculates the length of side $q$ ?

Question 7

A hiker travels $6$ km on a bearing of $040^{\circ}$ and then $10$ km on a bearing of $100^{\circ}$ . What is the hiker's distance from the starting point to the nearest kilometer?

Question 8

Ship $A$ is $5\text{ km}$ from a buoy on a bearing of $070^{\circ}$ . Ship $B$ is $8\text{ km}$ from the same buoy on a bearing of $110^{\circ}$ . What is the distance between the two ships?

Question 9

In triangle $ABC$ , the side lengths are $b = 4$ , $c = 6$ , and $a = \sqrt{28}$ . Determine the value of $\cos A$ .

Question 10

An explorer travels 10 km East (bearing $090^{\circ}$ ), then turns and travels 10 km on a bearing of $150^{\circ}$ . How far is the explorer from her starting point?

Type

Difficulty

Question 1

Question 2

A triangle has side lengths of $8$ , $11$ , and $15$ . Calculate the measure of the smallest angle in the triangle to one decimal place.

Question 3

A triangle has side lengths $a=4$ , $b=5$ , and $c=8$ . If you calculate $\cos C$ using the cosine rule, what does the resulting value indicate about angle $C$ ?

Question 4

To find the smallest angle in a triangle with side lengths $8, 15,$ and $17$ , which of the following fractions would be input into the inverse cosine function?

Question 5

For a triangle with side lengths $x$ , $y$ , and $z$ , let the angle opposite side $y$ be $Y$ . If $\cos Y < 0$ , which of the following mathematical relationships must be true?

Question 6

Question 7

A hiker travels $6$ km on a bearing of $040^{\circ}$ and then $10$ km on a bearing of $100^{\circ}$ . What is the hiker's distance from the starting point to the nearest kilometer?

Question 8

Ship $A$ is $5\text{ km}$ from a buoy on a bearing of $070^{\circ}$ . Ship $B$ is $8\text{ km}$ from the same buoy on a bearing of $110^{\circ}$ . What is the distance between the two ships?

Question 9

In triangle $ABC$ , the side lengths are $b = 4$ , $c = 6$ , and $a = \sqrt{28}$ . Determine the value of $\cos A$ .

Question 10

An explorer travels 10 km East (bearing $090^{\circ}$ ), then turns and travels 10 km on a bearing of $150^{\circ}$ . How far is the explorer from her starting point?

Type

Difficulty

Question 1

Question 2

A triangle has side lengths of $8$ , $11$ , and $15$ . Calculate the measure of the smallest angle in the triangle to one decimal place.

Question 3

A triangle has side lengths $a=4$ , $b=5$ , and $c=8$ . If you calculate $\cos C$ using the cosine rule, what does the resulting value indicate about angle $C$ ?

Question 4

To find the smallest angle in a triangle with side lengths $8, 15,$ and $17$ , which of the following fractions would be input into the inverse cosine function?

Question 5

For a triangle with side lengths $x$ , $y$ , and $z$ , let the angle opposite side $y$ be $Y$ . If $\cos Y < 0$ , which of the following mathematical relationships must be true?

Question 6

Question 7

A hiker travels $6$ km on a bearing of $040^{\circ}$ and then $10$ km on a bearing of $100^{\circ}$ . What is the hiker's distance from the starting point to the nearest kilometer?

Question 8

Ship $A$ is $5\text{ km}$ from a buoy on a bearing of $070^{\circ}$ . Ship $B$ is $8\text{ km}$ from the same buoy on a bearing of $110^{\circ}$ . What is the distance between the two ships?

Question 9

In triangle $ABC$ , the side lengths are $b = 4$ , $c = 6$ , and $a = \sqrt{28}$ . Determine the value of $\cos A$ .

Question 10

An explorer travels 10 km East (bearing $090^{\circ}$ ), then turns and travels 10 km on a bearing of $150^{\circ}$ . How far is the explorer from her starting point?

Cosine rule Questionbank