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:

$$\begin{gathered} K=angle(KL,KM) \\ {K}_1=\arccos ({\displaystyle \frac{-l_0\cdot m_0-l_1\cdot m_1}{l\cdot m}})=\arccos ({\displaystyle \frac{-(-10)\cdot 1-13\cdot (-22)}{16.4012\cdot 22.0227}})\doteq 0.6103 \\ K=K_1\to \text{ °}=K_1\cdot {\displaystyle \frac{180}{\pi }}\text{ °}=0.6103\cdot {\displaystyle \frac{180}{\pi }}\text{ °}=34.966\text{ °}=34.966\text{°}=34\mathrm{°}57^{\mathrm{\prime }}58\mathrm{"} \end{gathered}$$

$$\begin{gathered} L=angle(LK,LM) \\ {L}_1=\arccos ({\displaystyle \frac{k_0\cdot m_0+k_1\cdot m_1}{k\cdot m}})=\arccos ({\displaystyle \frac{(-9)\cdot 1+(-9)\cdot (-22)}{12.7279\cdot 22.0227}})\doteq 0.8308 \\ L=L_1\to \text{ °}=L_1\cdot {\displaystyle \frac{180}{\pi }}\text{ °}=0.8308\cdot {\displaystyle \frac{180}{\pi }}\text{ °}=47.603\text{ °}=47.6026\text{°}=47\mathrm{°}36^{\mathrm{\prime }}9\mathrm{"} \end{gathered}$$

$$\begin{gathered} M_1=\arccos ({\displaystyle \frac{k_0\cdot l_0+k_1\cdot l_1}{k\cdot l}})=\arccos ({\displaystyle \frac{(-9)\cdot (-10)+(-9)\cdot 13}{12.7279\cdot 16.4012}})\doteq 1.7005 \\ M=M_1\to \text{ °}=M_1\cdot {\displaystyle \frac{180}{\pi }}\text{ °}=1.7005\cdot {\displaystyle \frac{180}{\pi }}\text{ °}=97.431\text{ °}=97.4314\text{°}=97\mathrm{°}25^{\mathrm{\prime }}53\mathrm{"} \end{gathered}$$

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Showing 5 comments:

Math student

It's Great!. Am grateful.

3 years ago  1 Like Like

Math student

Still don't get it though

3 years ago  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

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I need one question

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