Calculate triangle

In the triangle, ABC, calculate the sizes of all heights, angles, perimeters, and areas if given a=40cm, b=57cm, and c=59cm.

Final Answer:

o = 156 cm
S = 1087.4907 cm²
v₁ = 54.3745 cm
v₂ = 38.1576 cm
v₃ = 36.8641 cm
A = 40.2961 °
B = 67.1615 °
C = 72.5424 °

Step-by-step explanation:

a = 40 cm b = 57 cm c = 59 cm o = a + b + c = 40 + 57 + 59 = 156 cm

s = o / 2 = 156 / 2 = 78 cm S = s \cdot (s - a) \cdot (s - b) \cdot (s - c) = 78 \cdot (78 - 40) \cdot (78 - 57) \cdot (78 - 59) = 11491 = 1087.4907 cm^{2}

S = \frac{a \cdot v _{1}}{2} v_{1} = 2 \cdot S / a = 2 \cdot 1087.4907 / 40 = 54.3745 cm

v_{2} = 2 \cdot S / b = 2 \cdot 1087.4907 / 57 = 491 = 38.1576 cm

v_{3} = 2 \cdot S / c = 2 \cdot 1087.4907 / 59 = 36.8641 cm

sin A = v_{3} : b = 36.8641 : 57 ≐ 0.6467 = 193909 : 299826 A = \frac{1 8 0 °}{π} \cdot arcsin (v_{3} / b) = \frac{1 8 0 °}{π} \cdot arcsin (36.8641 / 57) = 40.296 1^{\circ} = 40 ° 1 7^{'} 46 "

sin B = v_{3} : a = 36.8641 : 40 ≐ 0.9216 = 82159 : 89148 B = \frac{1 8 0 °}{π} \cdot arcsin (v_{3} / a) = \frac{1 8 0 °}{π} \cdot arcsin (36.8641 / 40) = 67.161 5^{\circ} = 67 ° 9^{'} 41 "

C = 180 - A - B = 180 - 40.2961 - 67.1615 = 72.542 4^{\circ} = 72 ° 3 2^{'} 33 "

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You need to know the following knowledge to solve this word math problem:

algebra

rearrange variables

planimetrics

goniometry and trigonometry

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Calculate triangle

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