Using a Ruler and a Protractor

Oct 13, 2025 by miodeya.com 99 views

Introduction

In this article, we will discuss how to make an accurate drawing of a triangle using a ruler and a protractor. We will also measure the length of side b in the drawing and provide the answer to 1 decimal place.

Step 1: Drawing the Triangle

To draw the triangle, we need to follow these steps:

Draw a line segment AB with a length of 7 cm.
Draw a line segment AC with a length of 8 cm.
Draw an angle of 30° at point A.

Using a Ruler and a Protractor

To draw the triangle accurately, we need to use a ruler and a protractor. A ruler is a straightedge with markings to measure lengths, while a protractor is a tool used to measure angles.

Using a Ruler: To draw the line segments AB and AC, we need to use a ruler. We can place the ruler along the edge of the paper and draw a line segment by moving the pencil along the ruler.
Using a Protractor: To draw the angle of 30° at point A, we need to use a protractor. We can place the protractor along the edge of the paper and draw a line segment by moving the pencil along the protractor.

Measuring Length b

To measure the length of side b, we need to use a ruler. We can place the ruler along the edge of the paper and measure the length of side b.

Calculating the Length of Side b

To calculate the length of side b, we need to use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides of a triangle.

The Law of Sines

The Law of Sines can be expressed as:

a / sin(A) = b / sin(B) = c / sin(C)

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite to the sides.

Applying the Law of Sines

To calculate the length of side b, we can apply the Law of Sines as follows:

b / sin(B) = a / sin(A)

where a is the length of side AB, B is the angle opposite to side b, and A is the angle opposite to side a.

Solving for b

To solve for b, we can rearrange the equation as follows:

b = a * sin(B) / sin(A)

Plugging in the Values

To plug in the values, we need to know the length of side AB, the angle opposite to side b, and the angle opposite to side a.

Length of Side AB: The length of side AB is 7 cm.
Angle Opposite to Side b: The angle opposite to side b is 30°.
Angle Opposite to Side a: The angle opposite to side a is 60°.

Calculating the Length of Side b

To calculate the length of side b, we can plug in the values as follows:

b = 7 * sin(30°) / sin(60°)

Simplifying the Expression

To simplify the expression, we can use the fact that sin(30°) = 0.5 and sin(60°) = √3/2.

Solving for b

To solve for b, we can simplify the expression as follows:

b = 7 * 0.5 / (√3/2)

Simplifying the Expression

To simplify the expression, we can cancel out the 2 in the denominator and numerator.

Solving for b

To solve for b, we can simplify the expression as follows:

b = 7 * 0.5 / (√3/2) b = 7 * 0.5 * 2 / √3 b = 7 / √3 b = 7 / 1.732 b = 4.04

Conclusion

In this article, we discussed how to make an accurate drawing of a triangle using a ruler and a protractor. We also measured the length of side b in the drawing and provided the answer to 1 decimal place.

References

"The Law of Sines." Math Open Reference, mathopenref.com/specialsinelaw.html.
"How to Draw a Triangle." wikiHow, wikihow.com/Draw-a-Triangle.

Q: What is the Law of Sines?

A: The Law of Sines is a mathematical concept that states that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides of a triangle.

Q: How do I use a protractor to draw an angle?

A: To use a protractor to draw an angle, place the protractor along the edge of the paper and align the angle with the protractor's markings. Then, draw a line segment by moving the pencil along the protractor.

Q: How do I measure the length of a side using a ruler?

A: To measure the length of a side using a ruler, place the ruler along the edge of the paper and align the edge of the ruler with the side you want to measure. Then, read the measurement from the ruler.

Q: What is the difference between a protractor and a compass?

A: A protractor is a tool used to measure angles, while a compass is a tool used to draw circles and arcs.

Q: How do I draw a triangle using a ruler and a protractor?

A: To draw a triangle using a ruler and a protractor, follow these steps:

Draw a line segment AB with a length of 7 cm.
Draw a line segment AC with a length of 8 cm.
Draw an angle of 30° at point A.

Q: How do I calculate the length of side b using the Law of Sines?

A: To calculate the length of side b using the Law of Sines, follow these steps:

Plug in the values into the equation: b = a * sin(B) / sin(A)
Simplify the expression using the fact that sin(30°) = 0.5 and sin(60°) = √3/2
Solve for b

Q: What is the length of side b in the triangle shown below?

A: The length of side b in the triangle shown below is 4.04 cm.

Q: How do I measure the length of side b in a triangle?

A: To measure the length of side b in a triangle, use a ruler to measure the length of the side and a protractor to measure the angle opposite to the side.

Q: What is the difference between a decimal place and a significant figure?

A: A decimal place is the number of digits after the decimal point in a number, while a significant figure is a digit that is reliable and certain.

Q: How do I round a number to 1 decimal place?

A: To round a number to 1 decimal place, look at the digit in the second decimal place. If it is 5 or greater, round up. If it is less than 5, round down.

Q: What is the importance of accuracy in drawing a triangle?

A: Accuracy is important in drawing a triangle because it ensures that the triangle is drawn correctly and that the measurements are reliable.

Q: How do I ensure accuracy when drawing a triangle?

A: To ensure accuracy when drawing a triangle, use a ruler and a protractor to draw the triangle and measure the lengths and angles.