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Subject Test Math 2

Question 18 of 28

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SAT Subject Test

The graph shows a pentagon with all sides of equal length in the x y plane. The vertices of the pentagon are labeled A, B, C, D, and E, clockwise, with A and E on the x-axis, and B, C, and D above the x-axis. Vertex A is to the left of vertex E, and the coordinates of vertex A are 1 comma 0.

In the figure above, A B C D E is a regular pentagon with side of length 2. What is the x-coordinate of D ?

Select an Answer

2.62

Correct Answer: 
No

3.62

Correct Answer: 
Yes

3.73

Correct Answer: 
No

3.90

Correct Answer: 
No

4.90

Correct Answer: 
No

The sum of the measures of the interior angles of a regular pentagon is equal to 3 cross times 180 equals 540 to the power of ring operator end exponent. Each interior angle has a measure of 108 to the power of ring operator end exponent. Using supplementary angles, angle D E F has a measure of 72 to the power of ring operator end exponent. You can use right triangle trigonometry to find the x-coordinate of point D.

The graph shows a pentagon with all sides of equal length in the x y plane. The vertices of the pentagon are labeled A, B, C, D, and E, clockwise, with A and E on the x-axis, and B, C, and D above the x-axis. Vertex A is to the left of vertex E, and the coordinates of vertex A are 1 comma 0. A dashed vertical line segment, D F, is drawn, where F is on the x-axis and to the right of vertex E. The length of side D E is labeled 2.

Since cos 72 to the power of ring operator end exponent equals fraction numerator E F over denominator 2 end fraction, E F equals 2 invisible times cos 72 to the power of ring operator end exponent is about 0.62. Since the length of each side of the pentagon is 2, the x-coordinate of point E is 3. Putting the information together tells us that the x-coordinate of point D is 3.62. The correct answer is (B).

Question Difficulty: 
hard