Triangle

Plane coordinates of vertices: K[19, -4] L[9, 13] M[-20, 8] give Triangle KLM.

Calculate its area and its interior angles.

Correct answer:

S = 271.5
K = 42.4317 °
L = 110.6831 °
M = 26.8851 °

x_{0} = 19 y_{0} = - 4 x_{1} = 9 y_{1} = 13 x_{2} = - 20 y_{2} = 8 L M = M - L = (k_{0}, k_{1}) k_{0} = x_{2} - x_{1} = (- 20) - 9 = - 29 k_{1} = y_{2} - y_{1} = 8 - 13 = - 5 K M = M - K = (l_{0}, l_{1}) l_{0} = x_{2} - x_{0} = (- 20) - 19 = - 39 l_{1} = y_{2} - y_{0} = 8 - (- 4) = 12 L K = K - L = (m_{0}, m_{1}) m_{0} = x_{0} - x_{1} = 19 - 9 = 10 m_{1} = y_{0} - y_{1} = (- 4) - 13 = - 17 k = k_{0}^{2} + k_{1}^{2} = (- 29)^{2} + (- 5)^{2} = 866 ≐ 29.4279 l = l_{0}^{2} + l_{1}^{2} = (- 39)^{2} + 1 2^{2} = 3185 ≐ 40.8044 m = m_{0}^{2} + m_{1}^{2} = 1 0^{2} + (- 17)^{2} = 389 ≐ 19.7231 s = \frac{k + l + m}{2} = \frac{2 9 . 4 2 7 9 + 4 0 . 8 0 4 4 + 1 9 . 7 2 3 1}{2} ≐ 44.9777 S = s \cdot (s - k) \cdot (s - l) \cdot (s - m) = 44.9777 \cdot (44.9777 - 29.4279) \cdot (44.9777 - 40.8044) \cdot (44.9777 - 19.7231) = \frac{5 4 3}{2} = 271 \frac{1}{2} = 271.5

K = a n g l e (K L, K M) K_{1} = arccos (\frac{- l _{0} \cdot m _{0} - l _{1} \cdot m _{1}}{l \cdot m}) = arccos (\frac{- ( - 3 9 ) \cdot 1 0 - 1 2 \cdot ( - 1 7 )}{4 0 . 8 0 4 4 \cdot 1 9 . 7 2 3 1}) ≐ 0.7406 K = K_{1} \to ° = K_{1} \cdot \frac{1 8 0}{π} ° = 0.7406 \cdot \frac{1 8 0}{π} ° = 42.432 ° = 42.431 7^{\circ} = 42 ° 2 5^{'} 54 "

L = a n g l e (L K, L M) L_{1} = arccos (\frac{k _{0} \cdot m _{0} + k _{1} \cdot m _{1}}{k \cdot m}) = arccos (\frac{( - 2 9 ) \cdot 1 0 + ( - 5 ) \cdot ( - 1 7 )}{2 9 . 4 2 7 9 \cdot 1 9 . 7 2 3 1}) ≐ 1.9318 L = L_{1} \to ° = L_{1} \cdot \frac{1 8 0}{π} ° = 1.9318 \cdot \frac{1 8 0}{π} ° = 110.683 ° = 110.683 1^{\circ} = 110 ° 4 0^{'} 59 "

M_{1} = arccos (\frac{k _{0} \cdot l _{0} + k _{1} \cdot l _{1}}{k \cdot l}) = arccos (\frac{( - 2 9 ) \cdot ( - 3 9 ) + ( - 5 ) \cdot 1 2}{2 9 . 4 2 7 9 \cdot 4 0 . 8 0 4 4}) ≐ 0.4692 M = M_{1} \to ° = M_{1} \cdot \frac{1 8 0}{π} ° = 0.4692 \cdot \frac{1 8 0}{π} ° = 26.885 ° = 26.885 1^{\circ} = 26 ° 5 3^{'} 7 "

Try calculation via our triangle calculator.

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Showing 5 comments:

Math student

It's Great!. Am grateful.

6 years ago 1 Like Like

Math student

Still don't get it though

6 years ago 1 Like Like

Math student

I find it hard ... But I think I will get there. ... Slowly but surely ...

5 years ago Like

Math student

I still dont understand

5 years ago Like

Math student

I need one question

4 years ago Like

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