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 previous question asked to find AB, which suggests that AB is a measurement or distance. The given answer is 8.46m, indicating that AB is 8.46 meters long.

Explanation

The previous question asked to find AB, which suggests that AB is a measurement or distance. The given answer is 8.46m, indicating that AB is 8.46 meters long.

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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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