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?

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The measure of the other 2 angles of a right angle triangle with side lengths 8, 15, and 17 are approximately 28° and 62°

The triangle is right angle triangle. This means it has on of its angles as 90 degrees.

The other 2 angles sum up to 90 degrees.

Using Pythagoras's theorem,

c² = a² + b²

where

c = hypotenuse

a and b are the other 2 legs.

The hypotenuse is the longest sides of a right angle triangle. Therefore, 17 is the hypotenuse side of the triangle.

Using trigonometric ratio,

sin ∅ = opposite / hypotenuse

∅ = sin⁻¹ 8 / 17

∅ = sin⁻¹ 0.47058823529

∅ = 28.0724869359

∅ ≈ 28°

The last angle will be 90 - 28 = 62°

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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,

                             ...................................................(1)

                  Where,  Opp - 8

                                 Hyp - 17

                  From equation (1),

                                       = 0.470588

                                       (0.470588)

                                    a = 28.072°

                     For angle b,

                                   ...................................................(1)

                  Where,  Opp - 15

                                 Hyp - 17

                  From equation (1),

                                       = 0.882352

                                       (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.