What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long? 9 units, 12 units 11 units, 10.2 units 4.9 units, 15.8 units 4.9 units, 14.2 units 5.2 units, 14.1 units

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What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long? 9 units, 12 units 11 units, 10.2 units 4.9 units, 15.8 units 4.9 units, 14.2 units 5.2 units, 14.1 units

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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You have one angle that is not the right angle and the length of the hypotenuse. All you need is two basic trigonometric rules to solve this. Let's call one of the sides x and the other y Imagine having a triangle with sides x, y and h. Where x is the adjacent and y is the opposite to your 19° angle. Cosine of any angle is the adjacent over the hypotenuse. So you can write the first equation like this: [ cos(19°)=x/15 ] now solve for x to get [ x=15cos(19°) ] or about 14.2 units (make sure that your calculator is in degree mode). The other side of the triangle can be solved similarly by knowing that the sine of any angle is the opposite over the hypotenuse. [ sin(19°)=y/15 ] and again solve for y to get [ y=15sin(19°) ] or about 4.9 units. Your answer is D. 4.9 units, 14.2 units All done.

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