Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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.

__

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.

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.