Soalan 1:
Tukarkan setiap sudut berikut dalam unit darjah dan minit.
(a) 37.80°
(b) 74.6°
(c) 58.1°
(d) 60.2°
(e) 41.5°
(f) 16.9°
(g) 5.4°
(h) 72.3°
Penyelesaian:
Sudut diukur dalam unit darjah ( ° ). Sudut juga boleh dinyatakan dalam unit darjah ( ° ), minit (‘ ) dan saat ( ” ) iaitu,
1° = 60′
1′ = 60”
(a)
$$ \begin{aligned} 37.80^{\circ} & =37^{\circ}+0.80^{\circ} \\ & =37^{\circ}+(0.80 \times 60)^{\prime} \\ & =37^{\circ} 48^{\prime} \end{aligned} $$
(b)
$$ \begin{aligned} 74.6^{\circ} & =74^{\circ}+0.6^{\circ} \\ & =74^{\circ}+(0.6 \times 60)^{\prime} \\ & =74^{\circ}+36^{\prime} \\ & =74^{\circ} 36^{\prime} \end{aligned} $$
(c)
$$ \begin{aligned} 58.1^{\circ} & =58^{\circ}+0.1^{\circ} \\ & =58^{\circ}+(0.1 \times 60)^{\prime} \\ & =58^{\circ}+6^{\prime} \\ & =58^{\circ} 6^{\prime} \end{aligned} $$
(d)
$$ \begin{aligned} 60.2^{\circ} & =60^{\circ}+0.2^{\circ} \\ & =60^{\circ}+(0.2 \times 60)^{\prime} \\ & =60^{\circ}+12^{\prime} \\ & =60^{\circ} 12^{\prime} \end{aligned} $$
(e)
$$ \begin{aligned} 41.5^{\circ} & =41^{\circ}+0.5^{\circ} \\ & =41^{\circ}+(0.5 \times 60)^{\prime} \\ & =41^{\circ}+30^{\prime} \\ & =41^{\circ} 30^{\prime} \end{aligned} $$
(f)
$$ \begin{aligned} 16.9^{\circ} & =16^{\circ}+0.9^{\circ} \\ & =16^{\circ}+(0.9 \times 60)^{\prime} \\ & =16^{\circ}+54^{\prime} \\ & =16^{\circ} 54^{\prime} \end{aligned} $$
(g)
$$ \begin{aligned} 5.4^{\circ} & =5^{\circ}+0.4^{\circ} \\ & =5^{\circ}+(0.4 \times 60)^{\prime} \\ & =5^{\circ}+24^{\prime} \\ & =5^{\circ} 24^{\prime} \end{aligned} $$
(h)
$$ \begin{aligned} 72.3^{\circ} & =72^{\circ}+0.3^{\circ} \\ & =72^{\circ}+(0.3 \times 60)^{\prime} \\ & =72^{\circ}+18^{\prime} \\ & =72^{\circ} 18^{\prime} \end{aligned} $$
Tukarkan setiap sudut berikut dalam unit darjah dan minit.
(a) 37.80°
(b) 74.6°
(c) 58.1°
(d) 60.2°
(e) 41.5°
(f) 16.9°
(g) 5.4°
(h) 72.3°
Penyelesaian:
Sudut diukur dalam unit darjah ( ° ). Sudut juga boleh dinyatakan dalam unit darjah ( ° ), minit (‘ ) dan saat ( ” ) iaitu,
1° = 60′
1′ = 60”
(a)
$$ \begin{aligned} 37.80^{\circ} & =37^{\circ}+0.80^{\circ} \\ & =37^{\circ}+(0.80 \times 60)^{\prime} \\ & =37^{\circ} 48^{\prime} \end{aligned} $$
(b)
$$ \begin{aligned} 74.6^{\circ} & =74^{\circ}+0.6^{\circ} \\ & =74^{\circ}+(0.6 \times 60)^{\prime} \\ & =74^{\circ}+36^{\prime} \\ & =74^{\circ} 36^{\prime} \end{aligned} $$
(c)
$$ \begin{aligned} 58.1^{\circ} & =58^{\circ}+0.1^{\circ} \\ & =58^{\circ}+(0.1 \times 60)^{\prime} \\ & =58^{\circ}+6^{\prime} \\ & =58^{\circ} 6^{\prime} \end{aligned} $$
(d)
$$ \begin{aligned} 60.2^{\circ} & =60^{\circ}+0.2^{\circ} \\ & =60^{\circ}+(0.2 \times 60)^{\prime} \\ & =60^{\circ}+12^{\prime} \\ & =60^{\circ} 12^{\prime} \end{aligned} $$
(e)
$$ \begin{aligned} 41.5^{\circ} & =41^{\circ}+0.5^{\circ} \\ & =41^{\circ}+(0.5 \times 60)^{\prime} \\ & =41^{\circ}+30^{\prime} \\ & =41^{\circ} 30^{\prime} \end{aligned} $$
(f)
$$ \begin{aligned} 16.9^{\circ} & =16^{\circ}+0.9^{\circ} \\ & =16^{\circ}+(0.9 \times 60)^{\prime} \\ & =16^{\circ}+54^{\prime} \\ & =16^{\circ} 54^{\prime} \end{aligned} $$
(g)
$$ \begin{aligned} 5.4^{\circ} & =5^{\circ}+0.4^{\circ} \\ & =5^{\circ}+(0.4 \times 60)^{\prime} \\ & =5^{\circ}+24^{\prime} \\ & =5^{\circ} 24^{\prime} \end{aligned} $$
(h)
$$ \begin{aligned} 72.3^{\circ} & =72^{\circ}+0.3^{\circ} \\ & =72^{\circ}+(0.3 \times 60)^{\prime} \\ & =72^{\circ}+18^{\prime} \\ & =72^{\circ} 18^{\prime} \end{aligned} $$
Soalan 2:
Nyatakan setiap nilai sudut berikut dalam unit darjah.
(a) 65° 54′
(b) 47° 42′
(c) 18° 12′
(d) 69° 24′
(e) 70° 6′
(f) 36° 36′
(g) 35° 30′
(h) 20° 18′
Penyelesaian:
(a)
$$ \begin{aligned} 65^{\circ} 54^{\prime} & =65^{\circ}+54^{\prime} \\ & =65^{\circ}+\left(\frac{54}{60}\right)^{\circ} \\ & =65^{\circ}+0.9^{\circ} \\ & =65.9^{\circ} \end{aligned} $$
(b)
$$ \begin{aligned} 47^{\circ} 42^{\prime} & =47^{\circ}+42^{\prime} \\ & =47^{\circ}+\left(\frac{42}{60}\right)^{\circ} \\ & =47^{\circ}+0.7^{\circ} \\ & =47.7^{\circ} \end{aligned} $$
(c)
$$ \begin{aligned} 18^{\circ} 12^{\prime} & =18^{\circ}+12^{\prime} \\ & =18^{\circ}+\left(\frac{12}{60}\right)^{\circ} \\ & =18^{\circ}+0.2^{\circ} \\ & =18.2^{\circ} \end{aligned} $$
(d)
$$ \begin{aligned} 69^{\circ} 24^{\prime} & =69^{\circ}+24^{\prime} \\ & =69^{\circ}+\left(\frac{24}{60}\right)^{\circ} \\ & =69^{\circ}+0.4^{\circ} \\ & =69.4^{\circ} \end{aligned} $$
(e)
$$ \begin{aligned} 70^{\circ} 6^{\prime} & =70^{\circ}+6^{\prime} \\ & =70^{\circ}+\left(\frac{6}{60}\right)^{\circ} \\ & =70^{\circ}+0.1^{\circ} \\ & =70.1^{\circ} \end{aligned} $$
(f)
$$ \begin{aligned} 36^{\circ} 36^{\prime} & =36^{\circ}+36^{\prime} \\ & =36^{\circ}+\left(\frac{36}{60}\right)^{\circ} \\ & =36^{\circ}+0.6^{\circ} \\ & =36.6^{\circ} \end{aligned} $$
(g)
$$ \begin{aligned} 35^{\circ} 30^{\prime} & =35^{\circ}+30^{\prime} \\ & =35^{\circ}+\left(\frac{30}{60}\right)^{\circ} \\ & =35^{\circ}+0.5^{\circ} \\ & =35.5^{\circ} \end{aligned} $$
(h)
$$ \begin{aligned} 20^{\circ} 18^{\prime} & =20^{\circ}+18^{\prime} \\ & =20^{\circ}+\left(\frac{18}{60}\right)^{\circ} \\ & =20^{\circ}+0.3^{\circ} \\ & =20.3^{\circ} \end{aligned} $$
Nyatakan setiap nilai sudut berikut dalam unit darjah.
(a) 65° 54′
(b) 47° 42′
(c) 18° 12′
(d) 69° 24′
(e) 70° 6′
(f) 36° 36′
(g) 35° 30′
(h) 20° 18′
Penyelesaian:
(a)
$$ \begin{aligned} 65^{\circ} 54^{\prime} & =65^{\circ}+54^{\prime} \\ & =65^{\circ}+\left(\frac{54}{60}\right)^{\circ} \\ & =65^{\circ}+0.9^{\circ} \\ & =65.9^{\circ} \end{aligned} $$
(b)
$$ \begin{aligned} 47^{\circ} 42^{\prime} & =47^{\circ}+42^{\prime} \\ & =47^{\circ}+\left(\frac{42}{60}\right)^{\circ} \\ & =47^{\circ}+0.7^{\circ} \\ & =47.7^{\circ} \end{aligned} $$
(c)
$$ \begin{aligned} 18^{\circ} 12^{\prime} & =18^{\circ}+12^{\prime} \\ & =18^{\circ}+\left(\frac{12}{60}\right)^{\circ} \\ & =18^{\circ}+0.2^{\circ} \\ & =18.2^{\circ} \end{aligned} $$
(d)
$$ \begin{aligned} 69^{\circ} 24^{\prime} & =69^{\circ}+24^{\prime} \\ & =69^{\circ}+\left(\frac{24}{60}\right)^{\circ} \\ & =69^{\circ}+0.4^{\circ} \\ & =69.4^{\circ} \end{aligned} $$
(e)
$$ \begin{aligned} 70^{\circ} 6^{\prime} & =70^{\circ}+6^{\prime} \\ & =70^{\circ}+\left(\frac{6}{60}\right)^{\circ} \\ & =70^{\circ}+0.1^{\circ} \\ & =70.1^{\circ} \end{aligned} $$
(f)
$$ \begin{aligned} 36^{\circ} 36^{\prime} & =36^{\circ}+36^{\prime} \\ & =36^{\circ}+\left(\frac{36}{60}\right)^{\circ} \\ & =36^{\circ}+0.6^{\circ} \\ & =36.6^{\circ} \end{aligned} $$
(g)
$$ \begin{aligned} 35^{\circ} 30^{\prime} & =35^{\circ}+30^{\prime} \\ & =35^{\circ}+\left(\frac{30}{60}\right)^{\circ} \\ & =35^{\circ}+0.5^{\circ} \\ & =35.5^{\circ} \end{aligned} $$
(h)
$$ \begin{aligned} 20^{\circ} 18^{\prime} & =20^{\circ}+18^{\prime} \\ & =20^{\circ}+\left(\frac{18}{60}\right)^{\circ} \\ & =20^{\circ}+0.3^{\circ} \\ & =20.3^{\circ} \end{aligned} $$