Geometry and TrigonometryVery hardTrig ratio in a similar triangle
Geometry and Trigonometry practice question
Right triangle JKL has legs JK = 9 and KL = 12, with the right angle at K. Triangle MNP is similar to triangle JKL, with the right angle at N and MN = 27. What is the value of tan M?
- A. 4/3Correct
- B. 3/4
- C. 4/5
- D. 9/12
Answer: A. 4/3
Similar triangles have equal corresponding angles, so tan M = tan J = KL/JK = 12/9 = 4/3. (The scale factor 3 gives NP = 36, and 36/27 = 4/3 as well.)
Why the other answers are wrong
- B. 3/4
- 3/4 is tan L (or tan P), the other acute angle.
- C. 4/5
- 4/5 is sin M (opposite over hypotenuse, 12/15).
- D. 9/12
- 9/12 is JK/KL, the tangent of angle L (or P), not of angle M.
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