Question

Determine the unknown measures of the triangle shown. Round to the nearest tenth, if necessary. x = in. y ≈ ° z ≈ ° A right triangle is shown. The hypotenuse has a length of x. The other 2 sides have lengths of 24 inches and 7 inches. The angle opposite to the side with length 7 inches is y, and the angle opposite to the side with length 24 inches is z.

Answer 1

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Answer:

• x = 25
• y = 16.3°
• z = 73.7°

Step-by-step explanation:

The length of the hypotenuse can be found using the Pythagorean theorem:

  x² = 7² +24² = 49 +576 = 625

  x = √625 = 25

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The angles can be found from the sine relation.

  Sin = Opposite/Hypotenuse

  sin(y) = 7/25

  y = arcsin(7/25) ≈ 16.3°

The acute angles in a right triangle are complementary, so ...

  z = 90° -16.3° = 73.7°