find $m\\angle c$.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n$m\\angle…

find $m\\angle c$.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n$m\\angle c = \\square ^\\circ$

find $m\\angle c$.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n$m\\angle c = \\square ^\\circ$

Answer

Explanation:

Step1: Identify sides relative to ∠C

In right triangle ( \triangle ABC ) (right-angled at ( A )):

  • Opposite side to ( \angle C ): ( AB = 6 )
  • Hypotenuse: ( BC = 9 )
  • Adjacent side to ( \angle C ): ( AC = 6 )

Step2: Choose trigonometric ratio

We use the sine function, since we know the opposite side and hypotenuse: ( \sin(\angle C) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{AB}{BC} ) Substitute values: ( \sin(\angle C) = \frac{6}{9} = \frac{2}{3} )

Step3: Calculate ∠C

Use inverse sine to find the angle: ( \angle C = \arcsin\left(\frac{2}{3}\right) ) Calculate the value (rounded to nearest tenth): ( \angle C \approx 41.8^\circ )

Answer:

( 41.8 )