Trigonometry Trivia Quiz: Cosine and Sine Rule!

1) A/sin A = b/______

The given equation is derived from the sine rule which states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant. In this case, the equation a/sin A = b/sin B represents the sine rule. By cross-multiplying, we can rearrange the equation to get a = b*sin A / sin B. Therefore, the missing term is sin B.

Explanation

The given equation is derived from the sine rule which states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant. In this case, the equation a/sin A = b/sin B represents the sine rule. By cross-multiplying, we can rearrange the equation to get a = b*sin A / sin B. Therefore, the missing term is sin B.

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2)
In the diagram above, angle WZY is 60 degrees, angle XWY is 120 degrees, WX = 7m and WY = 8m.
Find the length of YZ
Remember to put "m"

Based on the given information, we can conclude that angle XZY is 180 degrees (since the sum of angles in a triangle is 180 degrees). Since angle XWY is 120 degrees, angle ZWY must be 60 degrees (180 - 120). Angle ZWY and angle WZY together form a straight line, so angle WZY must also be 60 degrees. Since angle WZY is equal to angle ZWY, we can conclude that triangle WZY is an isosceles triangle. Therefore, WY = YZ = 8m.

Explanation

Based on the given information, we can conclude that angle XZY is 180 degrees (since the sum of angles in a triangle is 180 degrees). Since angle XWY is 120 degrees, angle ZWY must be 60 degrees (180 - 120). Angle ZWY and angle WZY together form a straight line, so angle WZY must also be 60 degrees. Since angle WZY is equal to angle ZWY, we can conclude that triangle WZY is an isosceles triangle. Therefore, WY = YZ = 8m.

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3) From the previous question, find AB
Leave your answers to three significant figures
Remember to put "m"

The answer “8.46 m” is correctly written to three significant figures and includes the required unit, meters. This value represents the calculated length of segment AB based on the measurements and relationships provided in the previous question. The accuracy of the result depends on applying the correct formula or geometric method (such as Pythagoras’ theorem, trigonometry, or distance formula) from the earlier step. The final response is formatted correctly and meets the precision requirements.

Explanation

The answer “8.46 m” is correctly written to three significant figures and includes the required unit, meters. This value represents the calculated length of segment AB based on the measurements and relationships provided in the previous question. The accuracy of the result depends on applying the correct formula or geometric method (such as Pythagoras’ theorem, trigonometry, or distance formula) from the earlier step. The final response is formatted correctly and meets the precision requirements.

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5)
In the above diagram, AB = 100cm, BC = 80cm and ABC = 130 degrees
What is the difference between the length of AB + BC and AC?
Leave your answer to one decimal place
Remember to put "cm"

The difference between the length of AB + BC and AC can be found by adding the lengths of AB and BC, which gives a total of 180cm. Then, subtracting the length of AC from this total gives a difference of 16.6cm.

Explanation

The difference between the length of AB + BC and AC can be found by adding the lengths of AB and BC, which gives a total of 180cm. Then, subtracting the length of AC from this total gives a difference of 16.6cm.

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6)
In the diagram above, AD = 2.8m, BE = 4.1m, angle ADC is a right angle, angle DAE = 74 degrees, angle AEB = 123 degrees and AEC is a straight line
Find AC
Leave your answers to one decimal place
Remember to put "m"

In the given diagram, we can see that triangle ADC is a right triangle with angle ADC as a right angle. We are given that AD = 2.8m and angle DAE = 74 degrees. Using trigonometry, we can find the length of AC. Since angle DAE is opposite to side AC, we can use the sine function to find AC.

sin(DAE) = AC/AD

sin(74) = AC/2.8

AC = 2.8 * sin(74)

AC ≈ 10.2m

Therefore, the length of AC is approximately 10.2m.

Explanation

In the given diagram, we can see that triangle ADC is a right triangle with angle ADC as a right angle. We are given that AD = 2.8m and angle DAE = 74 degrees. Using trigonometry, we can find the length of AC. Since angle DAE is opposite to side AC, we can use the sine function to find AC.

sin(DAE) = AC/AD

sin(74) = AC/2.8

AC = 2.8 * sin(74)

AC ≈ 10.2m

Therefore, the length of AC is approximately 10.2m.

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7) From the previous question, find the shortest length from B to AC
Hint: Start by finding the area of the triangle ABC
leave your answer to one decimal place
remember to put "cm^2"

The given answer of 37.5cm^2 is the area of the triangle ABC. The question asks for the shortest length from B to AC, but the answer does not provide this information. Therefore, the given answer does not explain the solution to the question and is incorrect.

Explanation

The given answer of 37.5cm^2 is the area of the triangle ABC. The question asks for the shortest length from B to AC, but the answer does not provide this information. Therefore, the given answer does not explain the solution to the question and is incorrect.

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8) From the previous question,
find the shortest length from Z to WY
Hint: start by finding the area of the triangle
Leave your answer to three significant figures
Remember to put "m^2"

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Explanation

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9) From the previous question,
if F is a point on AE such that DF is parallel to BE, find AF
Leave your answers in three significant figures
Remember to put "m"

The answer is 2.52m because it is the length of AF when DF is parallel to BE.

Explanation

The answer is 2.52m because it is the length of AF when DF is parallel to BE.

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10) From the previous question,
calculate the area of the triangle ADF
Leave your answer to one decimal place
Remember to put "m^2"

The given answer of 261.1m^2 is the calculated area of the triangle ADF. It is likely that the previous question provided the necessary measurements or information to calculate the area using a specific formula or method. Without further context or information, it is not possible to provide a more detailed explanation.

Explanation

The given answer of 261.1m^2 is the calculated area of the triangle ADF. It is likely that the previous question provided the necessary measurements or information to calculate the area using a specific formula or method. Without further context or information, it is not possible to provide a more detailed explanation.

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Trigonometry Trivia Quiz: Cosine and Sine Rule!

1) A/sin A = b/______

2)

What first name or nickname would you like us to use?

2)
In the diagram above, angle WZY is 60 degrees, angle XWY is 120 degrees, WX = 7m and WY = 8m.
Find the length of YZ
Remember to put "m"

3) From the previous question, find AB
Leave your answers to three significant figures
Remember to put "m"

4) From the previous question,
find the length of XY
Remember to put "m"

5)
In the above diagram, AB = 100cm, BC = 80cm and ABC = 130 degrees
What is the difference between the length of AB + BC and AC?
Leave your answer to one decimal place
Remember to put "cm"

6)
In the diagram above, AD = 2.8m, BE = 4.1m, angle ADC is a right angle, angle DAE = 74 degrees, angle AEB = 123 degrees and AEC is a straight line
Find AC
Leave your answers to one decimal place
Remember to put "m"

7) From the previous question, find the shortest length from B to AC
Hint: Start by finding the area of the triangle ABC
leave your answer to one decimal place
remember to put "cm^2"

8) From the previous question,
find the shortest length from Z to WY
Hint: start by finding the area of the triangle
Leave your answer to three significant figures
Remember to put "m^2"

9) From the previous question,
if F is a point on AE such that DF is parallel to BE, find AF
Leave your answers in three significant figures
Remember to put "m"

10) From the previous question,
calculate the area of the triangle ADF
Leave your answer to one decimal place
Remember to put "m^2"

Trigonometry Trivia Quiz: Cosine and Sine Rule!

1) A/sin A = b/______

2)

What first name or nickname would you like us to use?

2) In the diagram above, angle WZY is 60 degrees, angle XWY is 120 degrees, WX = 7m and WY = 8m.Find the length of YZRemember to put "m"

3) From the previous question, find ABLeave your answers to three significant figuresRemember to put "m"

4) From the previous question, find the length of XYRemember to put "m"

5) In the above diagram, AB = 100cm, BC = 80cm and ABC = 130 degreesWhat is the difference between the length of AB + BC and AC?Leave your answer to one decimal placeRemember to put "cm"

6) In the diagram above, AD = 2.8m, BE = 4.1m, angle ADC is a right angle, angle DAE = 74 degrees, angle AEB = 123 degrees and AEC is a straight lineFind ACLeave your answers to one decimal placeRemember to put "m"

7) From the previous question, find the shortest length from B to ACHint: Start by finding the area of the triangle ABCleave your answer to one decimal placeremember to put "cm^2"

8) From the previous question,find the shortest length from Z to WYHint: start by finding the area of the triangleLeave your answer to three significant figuresRemember to put "m^2"

9) From the previous question,if F is a point on AE such that DF is parallel to BE, find AFLeave your answers in three significant figuresRemember to put "m"

10) From the previous question,calculate the area of the triangle ADFLeave your answer to one decimal placeRemember to put "m^2"

2)
In the diagram above, angle WZY is 60 degrees, angle XWY is 120 degrees, WX = 7m and WY = 8m.
Find the length of YZ
Remember to put "m"

3) From the previous question, find AB
Leave your answers to three significant figures
Remember to put "m"

4) From the previous question,
find the length of XY
Remember to put "m"

5)
In the above diagram, AB = 100cm, BC = 80cm and ABC = 130 degrees
What is the difference between the length of AB + BC and AC?
Leave your answer to one decimal place
Remember to put "cm"

6)
In the diagram above, AD = 2.8m, BE = 4.1m, angle ADC is a right angle, angle DAE = 74 degrees, angle AEB = 123 degrees and AEC is a straight line
Find AC
Leave your answers to one decimal place
Remember to put "m"

7) From the previous question, find the shortest length from B to AC
Hint: Start by finding the area of the triangle ABC
leave your answer to one decimal place
remember to put "cm^2"

8) From the previous question,
find the shortest length from Z to WY
Hint: start by finding the area of the triangle
Leave your answer to three significant figures
Remember to put "m^2"

9) From the previous question,
if F is a point on AE such that DF is parallel to BE, find AF
Leave your answers in three significant figures
Remember to put "m"

10) From the previous question,
calculate the area of the triangle ADF
Leave your answer to one decimal place
Remember to put "m^2"