Perimeter 59

The circumference of a circular bed is 36 m. Find the length of the arc corresponding to the following central angles: 90°, 45°30′, 120°, 15°.

Final Answer:

o₁ =  9 m
o₂ =  4.55 m
o₃ =  12 m
o₄ =  1.5 m

Step-by-step explanation:

$$\begin{gathered} o=36\text{m} \\ \alpha =90{}^{\circ } \\ \beta =45°30^{\prime }=45°+\frac{30}{60}°=45.5°=45.5 \\ \gamma =120{}^{\circ } \\ \delta =15{}^{\circ } \\ \Phi =360{}^{\circ } \\ {o}_1=\frac{\alpha }{\Phi }\cdot o=\frac{90}{360}\cdot 36=\frac{90\cdot 36}{360}=\frac{3240}{360}=9\text{m} \end{gathered}$$

$o_2=\frac{\beta }{\Phi }\cdot o=\frac{45.5}{360}\cdot 36=4.55\text{m}$

$o_3=\frac{\gamma }{\Phi }\cdot o=\frac{120}{360}\cdot 36=\frac{120\cdot 36}{360}=\frac{4320}{360}=12\text{m}$

$o_4=\frac{\delta }{\Phi }\cdot o=\frac{15}{360}\cdot 36=\frac{15\cdot 36}{360}=\frac{540}{360}=1.5\text{m}$

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