Binibini

Binibini owns a triangular residential lot bounded by two roads intersecting at 70°. The sides of the lot along the road are 62m and 43m, respectively. Find the length of the fence needed to enclose the lot. (express answers to the nearest hundredths)

Correct answer:

o =  167.2 m

Step-by-step explanation:

$$\begin{gathered} a=62\text{m} \\ b=43\text{m} \\ \gamma =70{}^{\circ } \\ a-\gamma -b \\ {c}^2=a^2+b^2-2\cdot a\cdot b\cdot \cos \gamma \\ c=\sqrt{a^2+b^2-2\cdot a\cdot b\cdot \cos \gamma }=\sqrt{a^2+b^2-2\cdot a\cdot b\cdot \cos 70°}=\sqrt{62^2+43^2-2\cdot 62\cdot 43\cdot \cos 70°}=\sqrt{62^2+43^2-2\cdot 62\cdot 43\cdot 0.34202}=62.20409\text{m} \\ o=a+b+c=62+43+62.2041=167.2\text{m} \end{gathered}$$

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