Which set of numbers could represent the side lengths of a right triangle? O A. 2, 3, 4
O B.
4, 5, 6
OC. 6, 9,
9, 12
D. 8, 15,
15, 17

 D) 8, 15, 17

Step-by-step explanation:

In order for three side lengths to represent a right triangle, they must satisfy the Pythagorean Theorem: a² + b² = c²    where c is the largest side.

A) 2² + 3² = 4²

   4  +  9   = 16      

       13      = 16      FALSE

B) 4² + 5² = 6²

  16  + 25 = 36

       41     = 36       FALSE

C) 6² + 9² = 12²

   36 + 81 = 144

       117    = 144       FALSE

D) 8² + 15² = 17²

  64 + 225 = 289

       289    = 289     TRUE!

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

pay attention in your classes and concentrate the best thing you can do to raise your test scores is to pay attention when you're supposed to be learning the material: in class!

take good notes.

do your homework.

use mnemonics and other tricks.

do practice tests.

note: the best i know.