Trigonometry: Solving Right Triangles
 This is a free lesson from our course in Trigonometry In this lesson you'll learn with the help of several examples, how to solve right triangles. To solve a triangle means to know all three sides and three angles. When you know the ratios of the sides, you use the method of similar figures i.e. the method to use when solving an isosceles right triangle or a 30 -60 -90 triangle. When you do not know the ratio numbers, then you must use the ratios. You'll use here the concept those are previously learnt i.e. Pythagorean Theorem and properties of sines, cosines, and tangents. For example: find the missing sides of a triangle using the Pythagorean Theorem i.e. a2 + b2 = c2 where, a and b are two legs of a right triangle and c is its hypotenuse.  (More text below video...)
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(Continued from above) To find the missing angle of the triangle, you may use the angle-sum theorem (which states that three angles of a triangle add up to 180 ). Also for solving a right triangle, trigonometric ratios can be used, be it a sine, cosine, or tangent ratio which will depend on which side and angle(s) are given. The lower case letters represents the side lengths and the upper case letters represent angle measures. For example: to solve right triangle with b = 5 and c = 8, we may use the Pythagorean Theorem i.e. a2 + b2 = c2 to get value of a, which comes to a = 6.2. Then angle B can be determined by using the trigonometric ratio expressed by:
sin B = opposite/hypotenuse = 5/8
that gives value of B = 39 . Then use the angle-sum theorem to determine remaining angle A, which comes to 51 .

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