When we want to measure an angle without protractor we use three Trigonometry functions; sine, cosine and Tangent functions. They will help us to measure an angle in Right Triangle. For this we have to remember Ratio of these Functions.
Let us see how we can estimate angle measurements:
Step 1: First we have to determine the angle. If there are two line segments which are making an angle wider than a Right Angle then it is an Obtuse Angle. If angle is narrow opening angle then it is an Acute Angle. If two lines are perfectly perpendicular to each other then angle is a right angle or 90 degree angle.
Step 2: We make transpose of perpendicular on paper, and find the intersecting Point of two lines. As we find the Intersection point of these two lines we extend the lines from intersection points, if it is necessary.
Step 3: Now we have to determine the slopes of both lines.
Step 4: There is a formula which is used to estimate the angle measurement. The formula is:
tan θ = (m2 – m1) / (1 + (m1 m2)).
Here m1 and m2 are slopes of lines respectively.
Step 5: Now calculate the arc tan to determine the angle between these two lines. For example: Let us assume we have a pair of lines and slopes of these lines are 3 and ¼ respectively. Now we have to calculate the angle between these two lines.
Θ = tan-1(3 – 1/4) / (1 + (3*1/4)) = 57.5 degree.