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Calculating angle sizes

Given a trigonometric ratio, calculating angle sizes involves using the ‘inverse’ function. In other words, when you are given a trigonometric ratio for an angle, we can determine the size of the angle by using the ‘inverse’ function.

Let’s look at some examples calculating angle sizes-

Example 1 : Given tan θ = 3/7

θ = tan^-1~(3/7)

=  23.19859  or  23° 11′ 54.9″

θ = 23° 12′  (to the nearest minute)

 

Example 2 : Given sin θ = 0.5

θ = sin^-1(0.5)

= 30°

 

Example 3 : Given cos θ= sqrt{3}/2

θ = cos^-1~{sqrt{3}/2}

= 60°

 

Tip for scientific calculator:

Given cos θ = 15/17;

θ = cos^-1(15/17)

When using a scientific calculator to solve the above equation, use the following keys in this order:

Shift or 2nd followed by cos (15/17) = 28.07249 or 28° 4′, and finally DMS key.

angle calculation with a scientific calculator

 

Here’s how to do angle measurement