Triangle

Plane coordinates of vertices: K[9, 5] L[-4, 8] M[3, 20] give Triangle KLM.

Calculate its area and its interior angles.

Final Answer:

S = 88.5
K = 55.204 °
L = 72.7382 °
M = 52.0578 °

x_{0} = 9 y_{0} = 5 x_{1} = - 4 y_{1} = 8 x_{2} = 3 y_{2} = 20 L M = M - L = (k_{0}, k_{1}) k_{0} = x_{2} - x_{1} = 3 - (- 4) = 7 k_{1} = y_{2} - y_{1} = 20 - 8 = 12 K M = M - K = (l_{0}, l_{1}) l_{0} = x_{2} - x_{0} = 3 - 9 = - 6 l_{1} = y_{2} - y_{0} = 20 - 5 = 15 L K = K - L = (m_{0}, m_{1}) m_{0} = x_{0} - x_{1} = 9 - (- 4) = 13 m_{1} = y_{0} - y_{1} = 5 - 8 = - 3 k = k_{0}^{2} + k_{1}^{2} = 7^{2} + 1 2^{2} = 193 ≐ 13.8924 l = l_{0}^{2} + l_{1}^{2} = (- 6)^{2} + 1 5^{2} = 329 ≐ 16.1555 m = m_{0}^{2} + m_{1}^{2} = 1 3^{2} + (- 3)^{2} = 178 ≐ 13.3417 s = \frac{k + l + m}{2} = \frac{1 3 . 8 9 2 4 + 1 6 . 1 5 5 5 + 1 3 . 3 4 1 7}{2} ≐ 21.6948 S = s \cdot (s - k) \cdot (s - l) \cdot (s - m) = 21.6948 \cdot (21.6948 - 13.8924) \cdot (21.6948 - 16.1555) \cdot (21.6948 - 13.3417) = 88.5

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{- ( - 6 ) \cdot 1 3 - 1 5 \cdot ( - 3 )}{1 6 . 1 5 5 5 \cdot 1 3 . 3 4 1 7}) ≐ 0.9635 K = K_{1} \to ° = K_{1} \cdot \frac{1 8 0}{π} ° = 0.9635 \cdot \frac{1 8 0}{π} ° = 55.204 ° = 55.20 4^{\circ} = 55 ° 1 2^{'} 14 "

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{7 \cdot 1 3 + 1 2 \cdot ( - 3 )}{1 3 . 8 9 2 4 \cdot 1 3 . 3 4 1 7}) ≐ 1.2695 L = L_{1} \to ° = L_{1} \cdot \frac{1 8 0}{π} ° = 1.2695 \cdot \frac{1 8 0}{π} ° = 72.738 ° = 72.738 2^{\circ} = 72 ° 4 4^{'} 17 "

M_{1} = arccos (\frac{k _{0} \cdot l _{0} + k _{1} \cdot l _{1}}{k \cdot l}) = arccos (\frac{7 \cdot ( - 6 ) + 1 2 \cdot 1 5}{1 3 . 8 9 2 4 \cdot 1 6 . 1 5 5 5}) ≐ 0.9086 M = M_{1} \to ° = M_{1} \cdot \frac{1 8 0}{π} ° = 0.9086 \cdot \frac{1 8 0}{π} ° = 52.058 ° = 52.057 8^{\circ} = 52 ° 3^{'} 28 "

Try calculation via our triangle calculator.

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

Showing 5 comments:

Math student

It's Great!. Am grateful.

7 years ago 1 Like Like

Math student

Still don't get it though

7 years ago 1 Like Like

Math student

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

6 years ago Like

Math student

I still dont understand

6 years ago Like

Math student

I need one question

5 years ago Like

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