How do i find the value of the missing sides and angles

9514 1404 393

  sides, shortest to longest, are 11 (given), 11√3, 22

  angles, smallest to largest, are 30°, 60°, 90°

Step-by-step explanation:

This is a "special triangle," so you will have memorized the relations involved. Since it is a right triangle, the two acute angles are complementary. The one not shown is ...

  90° -60° = 30° . . . . measure of missing acute angle

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You have memorized that the side ratios in a 30°-60°-90° triangle are ...

  1 : √3 : 2

and you notice here that the given side is the short side (corresponding to "1"). So, the measures of the other two sides are ...

  11 × √3 = 11√3

  11 × 2 = 22

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In summary, side measures are 11, 11√3, and 22. Angle measures are 30°, 60°, 90°.

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If you haven't yet memorized the features of this special triangle, you can use trigonometry to find the missing lengths. The mnemonic SOH CAH TOA can be helpful in reminding you ...

  Cos = Adjacent/Hypotenuse

In this triangle, that means ...

  cos(60°) = 11/hypotenuse

  hypotenuse = 11/cos(60°) = 11/(1/2) = 22

The remaining leg (b) can be found using the sine or tangent relations, or the Pythagorean theorem.

  11² + b² = 22²

  b² = 484 -121 = 363

  b = √363 = 11√3

Of course, the sum of angles in the triangle is 180°, so the missing angle (A) is ...

  A + 60° +90° = 180°

  A = 180° -150° = 30°

Then the triangle sides are 11, 11√3, and 22. The triangle angles are 30°, 60°, and 90°.

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step-by-step explanation: