Triangle A B C is similar to triangle D E F , where angle A corresponds to angle D and

Question

Triangle A B C is similar to triangle D E F , where angle A corresponds to angle D and angle C corresponds to angle F . Angles C and F are right angles. If tan A = 50 7 , what is the value of tan E ?

Accepted Answer

The correct answer is 7 50 . It's given that triangle A B C is similar to triangle D E F , where angle A corresponds to angle D and angle C corresponds to angle F . In similar triangles, the tangents of corresponding angles are equal. Since angle A and angle D are corresponding angles, if tan A = 50 7 , then tan D = 50 7 . It's also given that angles C and F are right angles. It follows that triangle D E F is a right triangle with acute angles D and E . The tangent of one acute angle in a right triangle is the inverse of the tangent of the other acute angle in the triangle. Therefore, tan E = 1 tan D . Substituting 50 7 for tan D in this equation yields tan E = 1 50 7 , or tan E = 7 50 . Thus, if tan A = 50 7 , the value of tan E is 7 50 . Note that 7/50 and .14 are examples of ways to enter a correct answer.

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