The sides and the angles as follows:
Therefore,
∠A = 54.8°
∠B = 35.2°
∠C = 90°
a ≈ 65.37
b ≈ 46.64
c = 80
The triangle is a right angle triangle. Using trigonometric ratios, let's find a.
sin 54.8 = opposite / hypotenuse
sin 54.8 = a / 80
a = 80 sin 54.8
a = 65.3715918668
a ≈ 65.37
let's use Pythagoras theorem to find b.
c² = a² + b²
b² = c² - a²
b² = 80² - 65²
b² = 6400 - 4225
b² = 2175
b = √2175
b = 46.6368952654
b ≈ 46.64
let's find ∠B
∠A + ∠B + ∠C = 180°
∠B = 180 - 54.8 - 90
∠B = 35.2°
Therefore,
∠A = 54.8°
∠B = 35.2°
∠C = 90°
The sides are as follows:
a ≈ 65.37
b ≈ 46.64
c = 80
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