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find the legs of a30°-60°-90° triangle whose hypotenuse is 15 in.

Sagot :

sqdancefan

Answer:

  • 7.5 in
  • 7.5√3 ≈ 12.99 in

Step-by-step explanation:

You want the legs of a 30°-60°-90° triangle with hypotenuse 15 in.

Special triangle

A 30°-60°-90° triangle is one of two "special" right triangles often seen in trig and geometry problems. As you know, the ratio of side lengths in this triangle is ...

  1 : √3 : 2

Multiplying these ratio values by 7.5, we find the lengths of the sides of the given triangle to be ...

  7.5 : 7.5√3 : 15

The legs have lengths 7.5 inches and 7.5√3 ≈ 12.99 inches.

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Additional comment

The other special triangle is the isosceles right triangle, 45°-45°-90°. Its sides have the ratio 1 : 1 : √2.

If you haven't learned these triangles yet, you can figure the lengths using the trig relations:

  short side = hypotenuse × sin(30°) = 15×1/2 = 7.5 . . . inches

  longer side = hypotenuse × cos(30°) = 15×(√3)/2 = 7.5√3 . . . inches.

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