Question

Find the area of the given triangle to the nearest square unit. A =___ square units

Answer 1

We know that

the law of sinus established
a/sin A=b/sin B=c/sin C
so
A=30°
B=45°
b=10 units
a/sin A=b/sin B---------> a/sin 30=10/sin 45------> a=10*sin 30/sin 45
a=7.07 units
C=180-(A+B)-------> C=180-(75°)-----> C=105°
b/sin B=c/sin C--------> c=b*sin C/sin B----> c=10*sin 105/sin 45
c=13.66 units

Area=(1/2)*b*c*sin A-------> Area=(1/2)*10*13.66*sin 30°-----> 34.15 units ²

the area of triangle is 34 units²