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SAT数学:角度例题 3

2019-09-12 SAT-数学 阅读

SAT Question
Rank: Medium
Topic: Shape, Trigonometry

Below is a question from a recent SAT exam. It is a non-calculator question that would typically take a student 1-2 minutes to complete.

In the figure above, triangle ABC is similar to triangle DEF. What is the value of cos(E)?
(A)12/5
(B)12/13
(C)5/12
(D)5/13

To answer this question, we will use trigonometry. The shapes are similar which means they have the same angles. So we will work out the size of angle ABC and this will be equal to angle DEF.
For the trigonometric ratio cosine, we use the formula:

The longest side, the hypotenuse, is 13. And the side Adjacent (next to) the angle is 12.
Therefore, we get the equation.

And, as B and E are equal:

So our answer is B.

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