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Right triangles and trigonometry SAT question

Math · Geometry and Trigonometry · Hard · Answer it here, explanation included.

  • One angle is a right angle.
  • The measure of a second angle is x°.
  • The length of the hypotenuse is 23.
  • The length of the leg opposite the angle with measure x° is 16.
  • A note indicates the figure is not drawn to scale.

In the triangle shown, what is the value of ?

Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.

ExplanationShow

The correct answer is . In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In the triangle shown, the length of the side opposite the angle with measure is units and the length of the hypotenuse is units. Therefore, the value of  is . Note that 16/23, .6956, .6957, 0.695, and 0.696 are examples of ways to enter a correct answer.

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