Amsco Integrated Algebra I: Applications of the Sine and Cosine Ratios
 This is a free lesson from our course in Amsco's Integrated Algebra

 This lesson explains applications of sine and cosine ratios in solving problems. In earlier learning of tangent ratios where the lengths of the two legs of a right triangle are involved, it is not directly useful in solving problems in which the hypotenuse is involved. In such cases of the right triangle, where two ratios involve the hypotenuse are called the sine of an angle and the cosine of an angle. Sine ratio: In a right triangle, the ratio of the length of the side opposite to the acute angle to the length of the hypotenuse is called sine ratio of the acute angle. Cosine Ratio: In a right triangle, the ratio of the length of the side adjacent to the acute angle to the length of the hypotenuse is called cosine ratio of the acute angle. (More text below video...)
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 The Pythagorean Theorem Applications of the Tangent Ratio
 (Continued from above) These can be written as say Sin A and Cos A: Given: A is an acute angle of a right triangle, sin A = measure of leg opposite A /  measure of the hypotenuseandcos A = measure of leg adjacent to A / measure of the hypotenuse As symbolic representation:Sin A = a/c and cos A = b/c These ratios can help you solve problems in the following cases: • we know the length of one leg and the measure of one acute angle and want to find the length of the hypotenuse. • we know the length of the hypotenuse and the measure of one acute angle and want to find the length of a leg. • we know the lengths of the hypotenuse and one leg and want to find the measure of an acute angle. For example: Given - A ladder 30 feet long leans against a building and reaches a point 25 feet above the ground. You need to find to the nearest degree the angle that the ladder makes with the ground. You’ll solve the above problem using the steps like: In right triangle, ABC, AB, the length of the hypotenuse is 30 feet and BC, the side opposite A, is 25, feet. Since the problem involves A, BC (its opposite side), and AB (the hypotenuse), the sine ratio is used. sin A = opp / hyp = 25/30 sin A = 25/30A = 56.42690 Answer: To the nearest degree, the measure of the angle is 56. The video above will help understand using several examples, more about the applications of Sine and Cosine Ratios.

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