Answer:
segment YZ ≈ 19.4 in
angle X ≈ 85.3°
angle Z ≈ 26.7°
Explanation:
1) Given two side lenghts and one angle you can use sine law:
[tex] \frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c} [/tex]
2) Using the sides with length 43 in and 40in, and the corresponding opposite angles, Z and 68°, that leads to:
[tex] \frac{sinZ}{43} = \frac{sin68}{40} [/tex]
From which you can clear sinZ and get:
sinZ = 43 × sin(68) / 40 = 0.9967
⇒ Z = arcsine(0.9967) ≈ 85.36°
3) The third angle can be determined using 85.36° + 68° + X = 180°
⇒ X = 180° - 85.36° - 68° = 26.64°.
4) Finally, you can apply the law of sine to obtain the last missing length:
[tex] \frac{x}{sin(26.64)} = \frac{40}{sin(68)} [/tex]
From which: x = 40 × sin(26.64°) / sin(68°) = 19.34 in
The answer, then is:
segment YZ ≈ 19.4 in
angle X ≈ 85.3°
angle Z ≈ 26.7°
