A rhombus has sides 11cm long the shorter diagonal of the rhombus is 8cm long find the size of the smaller angles of the rhombus
1 answer:
Answer:
42.64°
Step-by-step explanation:
Note: A rhombus has all its sides equal, its opposite angle are equal, its has bigger and smaller diagonal, diagonal bisect the angles and diagonal bisect each other.
From the diagram attached,
sinθ = opposite/adjacent
sinθ = 4/11
θ = sin⁻¹(4/11)
θ = 21.32
Therefore, from the diagram,
The smaller angle of the rhombus = 2θ
The smaller angle of the rhombus = (2×21.32)
The smaller angle of the rhombus = 42.64°
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Answer:
m∠A = 30°
m∠B = 80°
m∠C = 70°
Step-by-step explanation:
By applying cosine rule in the given triangle,
b² = a² + c² - 2ac[cos(∠B)]
From the given triangle,
a = 14 m
b = 28 m
c = 24 m
(28)² = (14)² + (24)² - 2(14)(24)cos(B)
784 = 196 + 576 - 672cos(∠B)
cos(∠B) = 0.1786
∠B =
∠B = 79.71°
∠B = 80°
By applying sine rule in the given triangle,
sinA = 0.491958
A = 29.47°
A ≈ 30°
By applying triangle sum theorem,
m∠A + m∠B + m∠C = 180°
30° + 80° + m∠C = 180°
m∠C = 70°