Geometry/Chapter 19

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In order to solve a right triangle using Trig, a simple acronym is used. SOHCAHTOA. SOH, standing for sine (opposite/hypotneuse), CAH, standing for cosine (adjacent/hypotneuse), and TOA, standing for tangent (opposite/adjacent).

This work is mainly done using a calculator, since the formulas for sine, cosine, and tangent are not well known, or known at all for that matter.

To solve for angles of a right triangle, you would use the same method of SOHCAHTOA, except you use sin^-1 (opp/hyp), cos^-1(adj/hyp), and tan^-1(opp/adj)

[edit] Example Problems

Example One: Finding the Missing Parts of a Right Triangle

Find the missing angle and the sides in a right triangle with an acute angle of 38 degrees and an hypotenuse of 15 meters.

Solution:

           The other acute angle can be found by realizing that the sum of the angles of a triangle is always 180 degrees. Therefore,
           180 = 38 + 90 + m<B so m a = 15sin38 = 9.23 meters. To find the adjacent side 
           we use the cosine function and the formula cos38 = b/15 ==> b= 15cos38 = 11.82 meters.

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