Question

A triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem. What are the measure of the other 2 angles?
Plz help

Answer 1

The other 2 angles of given right angles are 61.93° and 28.072°, if a triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem.

Step-by-step explanation:

The given is,

                  Right angled triangle,

                  Side lengths are 8, 15, and 17  

Step:1

                 The given triangle is right angle triangle by the converse of Pythagorean theorem, so the trigonometric ratio,

                Ref the attachment,

                For angle a,

                             $Sin a = \frac{Opp}{Hyp}$...................................................(1)

                  Where,  Opp - 8

                                 Hyp - 17

                  From equation (1),

                                       $= \frac{8}{17}$

                                       = 0.470588

                                       $= sin^{-1}$(0.470588)

                                    a = 28.072°

                     For angle b,

                                   $Sin a = \frac{Opp}{Hyp}$...................................................(1)

                  Where,  Opp - 15

                                 Hyp - 17

                  From equation (1),

                                       $= \frac{15}{17}$

                                       = 0.882352

                                       $= sin^{-1}$(0.882352)

                                    b = 61.93°

Step:2

           Check for solution for right angle triangle,

                         90 ° = Other 2 angles

                         90 ° = a + b

                         90 ° = 28.072° + 61.93°

                         90 ° = 90 °

Result:

           The other 2 angles of given right angles are 61.93° and 28.07°, if a triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem.