Triangle

Plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3] give Triangle KLM.

Calculate its area and its interior angles.

Correct answer:

S = 103.5
K = 34.966 °
L = 47.6026 °
M = 97.4314 °

Step-by-step explanation:

x_{0} = 11 y_{0} = - 10 x_{1} = 10 y_{1} = 12 x_{2} = 1 y_{2} = 3 L M = M - L = (k_{0}, k_{1}) k_{0} = x_{2} - x_{1} = 1 - 10 = - 9 k_{1} = y_{2} - y_{1} = 3 - 12 = - 9 K M = M - K = (l_{0}, l_{1}) l_{0} = x_{2} - x_{0} = 1 - 11 = - 10 l_{1} = y_{2} - y_{0} = 3 - (- 10) = 13 L K = K - L = (m_{0}, m_{1}) m_{0} = x_{0} - x_{1} = 11 - 10 = 1 m_{1} = y_{0} - y_{1} = (- 10) - 12 = - 22 k = k_{0}^{2} + k_{1}^{2} = (- 9)^{2} + (- 9)^{2} = 92 ≐ 12.7279 l = l_{0}^{2} + l_{1}^{2} = (- 10)^{2} + 1 3^{2} = 269 ≐ 16.4012 m = m_{0}^{2} + m_{1}^{2} = 1^{2} + (- 22)^{2} = 485 ≐ 22.0227 s = \frac{k + l + m}{2} = \frac{1 2 . 7 2 7 9 + 1 6 . 4 0 1 2 + 2 2 . 0 2 2 7}{2} ≐ 25.5759 S = s \cdot (s - k) \cdot (s - l) \cdot (s - m) = 25.5759 \cdot (25.5759 - 12.7279) \cdot (25.5759 - 16.4012) \cdot (25.5759 - 22.0227) = \frac{2 0 7}{2} = 103 \frac{1}{2} = 103.5

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{- ( - 1 0 ) \cdot 1 - 1 3 \cdot ( - 2 2 )}{1 6 . 4 0 1 2 \cdot 2 2 . 0 2 2 7}) ≐ 0.6103 K = K_{1} \to ° = K_{1} \cdot \frac{1 8 0}{π} ° = 0.6103 \cdot \frac{1 8 0}{π} ° = 34.966 ° = 34.96 6^{\circ} = 34 ° 5 7^{'} 58 "

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{( - 9 ) \cdot 1 + ( - 9 ) \cdot ( - 2 2 )}{1 2 . 7 2 7 9 \cdot 2 2 . 0 2 2 7}) ≐ 0.8308 L = L_{1} \to ° = L_{1} \cdot \frac{1 8 0}{π} ° = 0.8308 \cdot \frac{1 8 0}{π} ° = 47.603 ° = 47.602 6^{\circ} = 47 ° 3 6^{'} 9 "

M_{1} = arccos (\frac{k _{0} \cdot l _{0} + k _{1} \cdot l _{1}}{k \cdot l}) = arccos (\frac{( - 9 ) \cdot ( - 1 0 ) + ( - 9 ) \cdot 1 3}{1 2 . 7 2 7 9 \cdot 1 6 . 4 0 1 2}) ≐ 1.7005 M = M_{1} \to ° = M_{1} \cdot \frac{1 8 0}{π} ° = 1.7005 \cdot \frac{1 8 0}{π} ° = 97.431 ° = 97.431 4^{\circ} = 97 ° 2 5^{'} 53 "

Try calculation via our triangle calculator.

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Showing 5 comments:

Math student

It's Great!. Am grateful.

4 years ago 1 Like Like

Math student

Still don't get it though

3 years ago 1 Like Like

Math student

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

2 years ago Like

Math student

I still dont understand

2 years ago Like

Math student

I need one question

2 years ago Like

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