HardMath· Geometry and Trigonometry· Right triangles and trigonometry· SPR
In the figure above, . If and , what is the length of ?
Correct answer: 6
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Explanation
The correct answer is 6. Since , and are both similar to 3-4-5 triangles. This means that they are both similar to the right triangle with sides of lengths 3, 4, and 5. Since , which is 3 times as long as the hypotenuse of the 3-4-5 triangle, the similarity ratio of to the 3-4-5 triangle is 3:1. Therefore, the length of (the side opposite to ) is , and the length of (the side adjacent to ) is . It is also given that . Since and , it follows that , which means that the similarity ratio of to the 3-4-5 triangle is 2:1 ( is the side adjacent to ). Therefore, the length of , which is the side opposite to , is .
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id cb_question_bank:66b2a315-253e-45e7-b1b3-62e0a2222ca9 · question 55bb437a · IBN 00615-DC
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