I’m pretty sure you’re familiar with a protractor.
If not, a protractor is usually used to measure an angle accurately.
What if there’s no protractor in hand? Worry no more because you can measure an angle even with no protractor.
Step 1: Get a ruler and measure the exact distance of both sides from the origin point of the angle (Should be the identical distance for both sides). Take a pen and paper to record all the measurements.
Step 2: Label the distance as “D” and mark the two points on the angle. It should be a length away from the point of origin. Labeling after you measure it will help you identify each angle point easily.
Step 3: Use the ruler again to find the accurate distance between the two points on the angle and record the measurements on the paper.
Step 4: You will need to label the measured distance between the two points as “E.” This is to differentiate it from the previous measurement you did. Failure to record will result in confusion while doing measurements and calculations later on.
Step 5: Apply this Sine Formula: Angle measure = 2 x arcsin (0.5 x e/d). Input the values you’ve measured previously for “D” and “E.”
Step 6: Furthermore, this formula is derived from the actual equation for the provided sine measures of the side of the right triangle. The angle’s sine should be equal to the measurement of the opposite side of the angle and divided by the measurement of the triangle’s hypotenuse.
Step 7: Solve the angle measure using your graphing calculator. Encode number “2” and press the multiplication symbol. Then press “arcsin” and the value that is half of “D” and “E.”
Step 8: Double-check the encoded values, then press “Enter” or the “=” sign to get the final answer or solution. Make sure you’ve encoded the right values correctly, or you will get the wrong answer.
Step 9: For this formula, you can also use the calculator’s second key to solve it. Just press “arcsin,” which you can see from the same key as the sin.
Step 10: You should get the final answer correctly as soon as you reach this step. If you have a protractor or plans to grab one, later on, you can verify your answer and check if they were accurate or not.
You can also bisect angles without a protactor
There’s a lot that you can do other than measuring without a protractor. Talking back going back to basics, you can also bisect angles without using a protractor. For a quick refresher, bisecting an angle means to divide the angle into two equal parts. That’s the line that you see that splits an angle into two equal parts.
Here’s how to bisect the angles without a protractor:
Step 1: Use a compass to and place it on the vertex of the angle, which is point B.
Step 2: You will need to draw an arc from across each arm of the angle.
Step 3: Position your compass on the point where it intersects an arm and draw another arc on the inside of the angle.
Step 4: Repeat the same process for the other arm without changing the compass’ width so that the two arms will intersect from each other.Step 5: By using a ruler, connect the vertex to the point where the arcs intersect, which is at point D. The bisector of ABC is DB.
Step 6: To bisect the angles, use your compass and ruler for accuracy.
Constructing Special Angles without a Protractor
Step 1: You will need to draw a line segment of points L and M.
Step 2: Draw an arc across LM that goes up over point L.
Step 3: Move the compass to the direction where the point of the arc intersects point LM. Make sure you did not change the width of the compass.
Step 4: Draw another arc that crosses the first arc that you drew.
Step 5: Then connect point L to the point where the two arcs meet.
Important things to remember
- Ensure that you make measurements accurately. It’s always recommended to conduct measurements at least twice to verify its correctness.
- It won’t hurt to compare your answers when using a protractor. This will help you practice and learn better.
There you have it! It might be easier to measure, bisect, and construct angles using protractors. However, it’s also good to note that you can actually do it without it. Your geometry skills will also improve once you start doing it manually. So the next time you don’t have a protractor, you’re good to go!