Triangle side angle

The triangle ABC determines the size of the sides a and b and the magnitudes of the interior angles β and γ, given c = 1.86 m, the median to side c is 2.12 m, and the angle alpha is 40 ° 12 '.

Final Answer:

a = 1.7865 m
b = 2.7436 m
β = 97.576 °
γ = 42.224 °

Step-by-step explanation:

c = 1.86 m m_{3} = 2.12 m α = 40 + 12 / 60 = \frac{2 0 1}{5} = 40.2^{\circ} m_{3}^{2} = (c / 2)^{2} + b^{2} - 2 (c / 2) b cos α k_{1} = cos (α) = cos (40.2 °) ≐ 0.7638 m_{3}^{2} = (c / 2)^{2} + b^{2} - 2 \cdot (c / 2) \cdot b \cdot k_{1} 2.1 2^{2} = (1.86 / 2)^{2} + b^{2} - 2 \cdot (1.86 / 2) \cdot b \cdot 0.76379602863464 - b^{2} + 1.421 b + 3.63 = 0 b^{2} - 1.421 b - 3.63 = 0 p = 1; q = - 1.421; r = - 3.63 D = q^{2} - 4 p r = 1.42 1^{2} - 4 \cdot 1 \cdot (- 3.63) = 16.5362765781 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 . 4 2 \pm 1 6 . 5 4}{2} b_{1, 2} = 0.71033 \pm 2.033241 b_{1} = 2.743571351 b_{2} = - 1.322910738 b = b_{1} = 2.7436 ≐ 2.7436 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 40.2 ° = 2.743 6^{2} + 1.8 6^{2} - 2 \cdot 2.7436 \cdot 1.86 \cdot cos 40.2 ° = 2.743 6^{2} + 1.8 6^{2} - 2 \cdot 2.7436 \cdot 1.86 \cdot 0.763796 = 1.786 = 1.7865 m

Our quadratic equation calculator calculates it.

β = \frac{1 8 0 °}{π} \cdot arccos (\frac{a ^{2} + c ^{2} - b ^{2}}{2 \cdot a \cdot c}) = \frac{1 8 0 °}{π} \cdot arccos (\frac{1 . 7 8 6 5 ^{2} + 1 . 8 6 ^{2} - 2 . 7 4 3 6 ^{2}}{2 \cdot 1 . 7 8 6 5 \cdot 1 . 8 6}) = 97.57 6^{\circ} = 97 ° 3 4^{'} 34 "

γ = 180 - α - β = 180 - 40.2 - 97.576 = 42.22 4^{\circ} = 42 ° 1 3^{'} 26 "

Try calculation via our triangle calculator.

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

algebra

arithmetic

square root

planimetry

goniometry and trigonometry

Units of physical quantities

Grade of the word problem

high school

We encourage you to watch this tutorial video on this math problem: video1 video2

Triangle side angle

Final Answer:

Step-by-step explanation:

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

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