Answer:
Correct answer: d₁ = 6.8
Step-by-step explanation:
where is:
larger diagonal d₁ = ?
rhombus side a = 4
smaller (acute) angle α = 64°
The adjacent angles in the rhombus are complementary, meaning that their sum is 180 degrees.
We calculate the greater obtuse angle:
β = 180° - 64° = 116° ⇒ β = 116°
The larger diagonal and the two sides of the rhombus form a obtuse triangle
We obtain the required larger diagonal using the cosine theorem:
d₁² = a² + a² - 2 · a² · cos β = 2 · a² - 2 · a² · cos β = 2 · a² ( 1 - cos β)
d₁² = 2 · a² ( 1 - cos β) = 2 · 4² ( 1 - cos 116°) = 32 ( 1 - (- 0.438))
d₁² = 32 · ( 1 + 0.438) = 46, 016 ⇒
d₁ = √46, 016 = 6.78 ≈ 6.8
d₁ = 6.8
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