Question

How do I find the values of x & y without using the Pythagorean theorem?

Answer 1

9514 1404 393

Answer:

  23) x=20; y=10√3

  24) x=4√2; y=8

  25) x=12; y=3+6√3

Step-by-step explanation:

Recognize that all of the triangles involved here are one of the two "special" triangles. By previous use of the Pythagorean theorem, or your familiarity with the trig functions of the "special" angles 30°, 45°, 60°, you know the following side ratios:

  45°-45°-90° triangle: 1 : 1 : √2

  30°-60°-90° triangle: 1 : √3 : 2

Using these ratios, you can solve these figures "by inspection."

__

23) x = 2((10√2)/√2) = 20

  y = √3((10√2)/√2) = 10√3

__

24) x = 4√2

  y = (4√2)√2 = 8

__

25) x = 6·2 = 12

y = 3 +6√3 . . . . . 3 units more than the longer leg of the 6 : 6√3 : 12 triangle