# SAT Math Multiple Choice Question 727: Answer and Explanation

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**Question: 727**

**7.**

*Note:* Figure not drawn to scale.

In the figure above, *BCDE* is a rectangle, *AC* = 14, *BC* = 12, and *EC* = 13. What is the value of tan *x*?

- A. 0.4
- B. 0.6
- C. 1.3
- D. 2.5

**Correct Answer:** A

**Explanation:**

**A**

**Advanced Mathematics (triangle trigonometry) EASY**

First, let's mark up the diagram with the given lengths, as above. Remember from SOH CAH TOA that the tangent of an angle is equal to the opposite side over the adjacent side, so tan *x* = *AB/EB. AB* = *AC* - *BC* = 14 - 12 = 2, and we can find *EB* with the Pythagorean Theorem:

*EB*^{2} + 12^{2} = 13^{2}

Simplify:

*EB*^{2} + 144 = 169

Subtract 144:

*EB*^{2} = 25

Take the square root:

*EB* = 5

Or, even better, just notice that triangle *EBC* is a 5-12-13 triangle.

So, tan *x* = *AB/EB* = 2/5 = 0.4