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Trigonometric Ratios in Geometry

Updated on October 4, 2010

Trigonometric Ratios


In this hub we are going to be looking at the trigonometric ratios. Here we have a right angled triangle and the angle has been marked as “theta”.



So this symbol equals theta, one of the letters of the Greek alphabet.


Now we will name the sides of the triangle in relation to the symbol theta.

The hypotenuse is always the longest side in a right angled triangle.

Directly across from theta is called the opposite side



The side next to “theta “is named the adjacent side






Sin theta







Cos theta







Tan theta





Sine - Sin S O/H

Cosine - Cos C A/H

Tangent - Tan T O/A



These are the Trigonometric Ratios


You will have to memorise these


An easy way is;

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        S O/H                           C A/H                              T O/A




For the triangle on the right find;

  • Sin θ =


  • Tan θ =


  • Cos θ =


1. Sin θ = S O/H = 8 / 10

2. Tan θ = T O/A = 8 / 6

3. Cos θ = C A/H = 6 / 10




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    • t.elia profile image

      t.elia 4 years ago from Northern Ireland

    • profile image

      Varsha 7 years ago


      Need i more help from you.

      I tried searching sin theta table for multiples of 5 on internet which is in fractions. Like sin theta 75 degree, 80 degree etc in fractions. But the search showed sin theta table in decimals. Do you have one with fractions?

      My purpose is to learn these fractions so as to answer area of triangle questions by the 1/2 ab sin theta formula, where a & b are the sides and theta is the angle between them.

      Also are there any other trigonometric formulas for finding areas of geometric figures?

    • profile image

      kia 7 years ago

      thinks that wuz very hel[ful

    • t.elia profile image

      t.elia 7 years ago from Northern Ireland

      Thanks scooter

    • profile image

      scooter 7 years ago

      Useful information

    • t.elia profile image

      t.elia 7 years ago from Northern Ireland

      I am working on a hub at the moment for finding the side,using trigonometry. I hope to have it ready for publishing first thing in morning. Meanwhile keep revising and Good Luck in your exams.