Given the triangle below, what is m triangleA, rounded to the nearest tenth?
2 answers:
Answer:
The correct answer is option A 17.8°
Step-by-step explanation:
From the figure attached with this answer,
We can see a perpendicular from B to side AC
<u>To find BD</u>
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
<u>To find the value of m<A</u>
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°
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