Calculate 82696

In the triangle ABC, b=5 cm, c=6 cm, /BAC/ = 80° are given. Calculate the sizes of the other sides and angles, and further determine the sizes of the tangent tc and the area of the triangle.

Correct answer:

a = 7.112 cm
β = 43.8166 °
γ = 56.1834 °
t = 5.3657 cm
S = 14.7721 cm²

Step-by-step explanation:

b = 5 cm c = 6 cm α = 80^{\circ} a^{2} = b^{2} + c^{2} - 2 \cdot b \cdot c \cdot cos α a = b^{2} + c^{2} - 2 \cdot b \cdot c \cdot cos α = b^{2} + c^{2} - 2 \cdot b \cdot c \cdot cos 80 ° = 5^{2} + 6^{2} - 2 \cdot 5 \cdot 6 \cdot cos 80 ° = 5^{2} + 6^{2} - 2 \cdot 5 \cdot 6 \cdot 0.173648 = 7.112 = 7.112 cm

b^{2} = a^{2} + c^{2} - 2 \cdot a \cdot c \cdot cos β B = arccos (\frac{a ^{2} + c ^{2} - b ^{2}}{2 \cdot a \cdot c}) = arccos (\frac{7 . 1 1 2 ^{2} + 6 ^{2} - 5 ^{2}}{2 \cdot 7 . 1 1 2 \cdot 6}) ≐ 0.7647 rad β = B \to ° = B \cdot \frac{1 8 0}{π} ° = 0.7647 \cdot \frac{1 8 0}{π} ° = 43.817 ° = 43.816 6^{\circ} = 43 ° 4 9^{'}

γ = 180 - α - β = 180 - 80 - 43.8166 = 56.183 4^{\circ} = 56 ° 1 1^{'}

Try calculation via our triangle calculator.

t^{2} = b^{2} + (c / 2)^{2} - 2 \cdot b \cdot (c / 2) \cdot cos α) t = b^{2} + (c / 2)^{2} - b \cdot c \cdot cos α = b^{2} + (c / 2)^{2} - b \cdot c \cdot cos 80 ° = 5^{2} + (6 / 2)^{2} - 5 \cdot 6 \cdot cos 80 ° = 5^{2} + (6 / 2)^{2} - 5 \cdot 6 \cdot 0.173648 = 5.366 = 5.3657 cm

s = \frac{a + b + c}{2} = \frac{7 . 1 1 2 + 5 + 6}{2} ≐ 9.056 cm S = s \cdot (s - a) \cdot (s - b) \cdot (s - c) = 9.056 \cdot (9.056 - 7.112) \cdot (9.056 - 5) \cdot (9.056 - 6) = 14.7721 cm^{2}

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