InterviewSolution
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InterviewSolution
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In triangle ABC, the measure of B is 90%,BC 16, and AC-20. Triangle DE F is similar totriangle ABC, where vertices D, E, and Fcorrespond to vertices A, B, and C, respectively,and each side of triangle DE F is the length ofthe corresponding side of triangle ABC. What isthe value of sinF? |
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Answer» Triangle ABC is a right triangle with its right angle at B. Therefore, AC is the hypotenuse of right triangle ABC, and AB and BC are the legs of right triangle ABC. According to the Pythagorean theorem, AB=√202−162=√400−256=√144=12 Since triangle DEF is similar to triangle ABC, with vertex F corresponding to vertex C, the measure of angle∠F equals the measure of angle∠C. Therefore, sinF=sinC. From the side lengths of triangle ABC, sinF=oppositesidehypotenuse=AB/AC=12/20=3/5 Therefore, sinF=3/5. The final answer is 3/5 or 0.6. |
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