Answer:
The correct answer is option A 17.8°
Explanation:
From the figure attached with this answer,
We can see a perpendicular from B to side AC
To find BD
In triangle BDC, its angles are 30°, 60° and 90°
Therefore the sides are in the ratio 1 :√3 : 2
Here BC = 11
BD : DC : BC = 1 :√3 : 2 = 11√3/2 : 11/2 : 11
Therefore BD = 11/2
To find the value of m<A
We have
Sin ∅ = Opposite side /Hypotenuse
AB = 18 and BD = 11/2
Sin A = BD/AB =(11/2)/18 = 11/36 = 0.3055
m<A = Sin⁻¹(0.3055) = 17.79 ≈ 17.8°
Therefore the correct answer is option A 17.8°