Answer:
C
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] product of 2 sides × sin ( angle between the 2 sides )
We are only given 1 side (AC) so require to find AB or BC using the Sine rule
the third angle B = 180° - (48 + 67)° = 180° - 115° = 65°
using the Sine rule to find AB
[tex]\frac{AB}{sin67}[/tex] = [tex]\frac{15}{sin65}[/tex] ( cross- multiply )
AB × sin65° = 15 × sin67° ( divide both sides by sin65° )
AB = [tex]\frac{15sin67}{sin65}[/tex]
Now
A = [tex]\frac{1}{2}[/tex] × AB × AC sin48°
= [tex]\frac{1}{2}[/tex] × [tex]\frac{15sin67}{sin65}[/tex] × 15sin48°
= [tex]\frac{15sin67}{2sin65}[/tex] × 15sin48° → C
