How do you measure an angle without using a protractor?

Answer 1

You can easily work out, an exact value for an angle using trigonometry... The science of triangles.. I actually put the formulas into an MS spreadsheet so all i had to do was put the length of the sides into the database...

Trigonometry requires, certain information and you can adjust your formulae based on what info you have... Kinda like a Crime Scene Case... You can put the figures together...

Lets just say I have a triangle don't know any of the angles to it... But i can easily measure the sides.. also known as an SSS triangle... Although it doesn't necessarily need to be a triangle you can turn anything into a triangle...

So going back to what i was saying...

You got a Triangle with sides 10 by 12 by 14

Lets work out Angle [A] : (b²+c²-a²) /(2*b*c) then Cos-1(Answer)

So to work out angle A (10²+14²-12²) / (2*10*14) = 0.5428571 Then click the Cos-1(0.5428571) and you get 57.12 Degrees which is Angle A

To get the other Angles you simply alter the existing formula above..

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To work out Angle B simply change (b²+c²-a²) to (a²+c²-b²) and "/2*b*c" to "/(2*a*c)" and cos-1() it... Just remember you have Cos() on your calc but press your shift key to get Cos-1() it will make a difference... Cos-1 is the inverse number...

Now to get the last Angle either, Add Angles A+B togethor which we have worked out the Angles for, then take it away from 180 degrees or use the formula to work it out... I often do both just to verify my formula is correct...

One more thing... You may not have that specific triangle but there are numerous pieces of information that you might have... And i can reassure you that theres a few websites which will have the solution for the pieces of info you do have... Kinda like a Jigsaw... you just need to figure out which piece fits where.... Hope that helps... Its probs a lot simpler than it sounds when you work it out... Just message me if you have any probs...

that works but you need to have a ruler or the measurements of at least two sides to be able to use cos, sin, or tan. There are many different ways to calculate the measurements of an angle if you have a certain amount of information...It depends on what you have.