Answer:
SinB = 1/2, SinC = √3/2 and
TanC = √3
Step-by-step explanation:
The question lacks options. Find the complete question in the comment section.
Given triangle ABC, we will use the SOH, CAH, TOA trig identity to get the correct ratio.
Given the hypotenuse BC = 18 and one of the other two sides AC = 9, we can get the third side AB using Pythagoras theorem.
BC² = AC²+AB²
18² = 9²+AB²
2² = 1²+AB²
AB² = 4-1
AB² = 3.
AB = √3
Making <ABC as reference angle, AC will be opposite and AB will be the adjacent.
Sin<ABC = opp/hyp = AC/BC
Sin<ABC = 1/2
Cos<ABC = adj/hyp = AB/BC
Cos<ABC = √3/2
Tan<ABC = opp/adj = AC/AB
Tan<ABC = 1/√3
Making <BCA as reference angle, AB will be opposite and AC will be the adjacent.
Sin<BCA = opp/hyp = AB/BC
Sin<BCA = √3/2
Cos<BCA = adj/hyp = AC/BC
Cos<BCA = 1/2
Tan<BCA = opp/adj = AC/AB
Tan<BCA = √3
Frim the above calculation, the correct options are sin<ABC = 1/2, Sin<BCA = √3/2 and Tan<BCA = √3
