Question

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Answer 1

Hello,
Please, see the detailed solution in the attached file.
Thanks.

Answer 2

1) You have:
 Cos(50°)=adjacent/hypotenuse
 Cos(50°)=XY/8
 Solve for XY:
 XY=8Cos(50°)
 XY=8 cm
 The answer is 8 cm

 2)The angle m∠A is:
 Cos^-1(m∠A)=8/15
 m∠A=57.76°

 The angle m∠C is:
 Sin⁻1(m∠C)=8/15
 m∠C=32.23°

 The approximate difference is:
 m∠A-m∠C≈25.53°

 The answer is: The approximate difference between m∠A and m∠C is 25.53°.