Answer:
D. 17.61 square units
Step-by-step explanation:
To find the area of the ∆ABC, we can apply the formula below:
Area of ∆ABC = ½×a×c×sin(B)
a = 10
c = ??
B = 22°
Let's find c using Sine Rule:
Thus:
[tex] \frac{a}{sin(A)} = \frac{c}{sin(C)} [/tex]
Where,
a = 10
c = ??
A = 180 - (22 + 70) = 88°
C = 70°
Plug in the values
[tex] \frac{10}{sin(88)} = \frac{c}{sin(70)} [/tex]
Multiply both sides by sin(70)
[tex] \frac{10}{sin(88)} \times sin(70) = \frac{c}{sin(70)} \times sin(70) [/tex]
[tex] \frac{10 \times sin(70)}{sin(88)} = c [/tex]
[tex] 9.4 = c [/tex] (nearest tenth)
✔️Area of ∆ABC = ½×a×c×sin(B)
Plug in the values
Area of ∆ABC = ½ × 10 × 9.4 × sin(22)
Area = 17.61 square units (nearest tenth)
