Triangle X Y Z is shown. Angle X Y Z is 51 degrees and angle Y Z X is 76 degrees. The length of X Z is 2.6, the length of X Y is
z, and Y Z is x. Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction Which equation is correct and can be used to solve for the value of z? StartFraction sine (51 degrees) Over 2.6 EndFraction = StartFraction sine (76 degrees) Over z EndFraction StartFraction sine (51 degrees) Over 2.6 EndFraction = StartFraction sine (53 degrees) Over z EndFraction StartFraction sine (76 degrees) Over 2.6 EndFraction = StartFraction sine (51 degrees) Over z EndFraction StartFraction sine (76 degrees) Over 2.6 EndFraction = StartFraction sine (53 degrees) Over z EndFraction
ITS A
ITS A
2 answers:
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Answer:
x = 5
Step-by-step explanation:
Since ∠P ≅ ∠P and ∠PST≅ ∠PRQ (corresponding angles are congruent when the lines are parallel), ΔPST is similar to ΔPRQ by the AA postulate
Therefore, corresponding sides are in proportion.
PS ↔ PR and ST ↔ RQ
Note: PR = PS + SR = x + 7 + x - 1 = 2x + 6
8(x + 7) = 6(2x + 6)
8x+56 = 12x + 36
4x = 20
x = 5