PLEASE HELP WILL GIVE 25 PTS IN A SEPERATE QUESTION TO CORRECT ANSWER TRIG/GEO!!!

In ΔXYZ, x = 8.3 meters, y = 9 meters, and z = 15 meters. Find the remaining measurements of the triangle, and round your answers to the nearest tenth.

∠X = 56.9°, ∠Y = 66.6°, ∠Z = 56.5°
∠X = 28.6°, ∠Y = 31.2°, ∠Z = 120.2°
∠X = 56.9°, ∠Y = 66.6°, ∠Z = 120.2°
∠X = 28.6°, ∠Y = 31.2°, ∠Z = 56.5°

∠X = 28.6° , ∠Y = 31.2° ,  ∠Z =120.2°

Step-by-step explanation:

Using the cosine rule, we can find one angle, then using that one anle, we can find the next angle by sine rule.

z² = x² + y² - 2(x)(y) cos (Z)

15² = 8.3² + 9² - 2(8.3)(9) cos (Z)

225 = 68.89 + 81 - 149.4 cos (Z)

Grouping the terms as,

225 - 68.89 - 81 = -149.4 cos (Z)

75.11 = -149.4 cos (Z)

cos (Z) = 75.11 / -149.4

       = - 0.5

cos⁻¹ (-0.5) = 120.2°

Now we can use the sine rule as,

sin X / x  = sin Z / z

To find sin X, we can rearrange the expression as,

sin X = x × sin Z / z

Plugin the values, we will get,

sin X =  8.3 × sin  120. 2 / 15

X = sin⁻¹ (0.4782) = 28.6°

As we all know that the sum of angles in a triangle is 180°.

∠X + ∠Y + ∠Z = 180°

28.6° + ∠Y + 120.2° = 180°

180° - 28.6° - 120.2° = 31.2° = ∠Y    

∠X = 28.6°, ∠Y = 31.2°, ∠Z = 120.2°

Step-by-step explanation:

this was on my test and it was right

step-by-step explanation: