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Mengenal Sudut

Ini merupakan bagian dari daftar isi Materi Garis dan Sudut Kelas 7.  Kita akan membahas tentang sudut dan cara menentukan besar sudut yang dibentuk oleh jarum jam. 

Konsep Sudut

Dalam kehidupan sehari-hari, banyak kita lihat sudut yang dibentuk oleh dua objek lurus yang bertemu pada satu titik. Misalnya pemanah, ada sudut yang terbentuk antara tangan dengan badan pemanah. Sudut terbentuk dari dua sinar garis bertemu pada satu titik. Sinar garis adalah objek geometris berupa garis yang memiliki awal dan tidak memiliki titik ujung. Perhatikan gambar sudut berikut ini.

Tampak pada gambar di atas, sudut ialah daerah yang dibatasi oleh dua sinar garis yang terbatas pada titik sudut. Kita dapat melihat bahwa sudut terbentuk dari perpotongan dua sinar garis yang berpotongan tepat di satu titik, sehingga titik potongnya disebut dengan titik sudut.

Nama suatu sudut dapat berupa simbol α, β, dll, atau berdasarkan titik-titik yang melalui garis yang berpotongan tersebut. Biasanya, satuan sudut dinyatakan dalam dua jenis, yaitu derajat ("°") dan radian (rad). ∠APB bisa juga disebut ∠P, dan besar sudut P dilambangkan dengan m∠P dimana besar sudut satu putaran penuh adalah 360°.

Ada pertanyaan, apakah terbentuknya suatu sudut hanya didapat dari dua sinar garis atau apakah dua garis yang saling berimpitan juga memiliki besar sudut? Jika kita merujuk pada konsep sudut maka dua garis yang berimpit tentunya dapat membentuk sudut karena terdapat perpotongan pada suatu titik dari dua garis yang berbeda dan kita katakan besar sudut yang terbentuk adalah 0°.

Menentukan Besar Sudut yang Dibentuk oleh Jarum Jam

Dapatkah kalian menentukan besar sudut yang dibentuk oleh jarum jam. Misalnya besar sudut yang terbentuk ketika jarum pada jam menunjukkan pukul 02.00?

Silahkan digambar dulu jarum yang menunjukkan pukul 02.00. Dengan memperhatikan gambar kamu, kamu dapat melihat bahwa pada pukul 02.00, jarum jam menunjuk ke arah bilangan 2 dan jarum menit menunjuk ke arah bilangan 12, sehingga sudut yang terbentuk adalah 2/12 atau 1/6 putaran penuh, sehingga besar sudut yang terbentuk adalah $\frac{1}{6}×360°=60°$. 

Selanjutnya, mari kita cermati pengukuran sudut yang terbentuk oleh jarum jam dan jarum menit pada waktu-waktu yang lain. Diketahui perputaran selama 12 jam sebesar 360°, akibatnya pergeseran tiap satu jam adalah $\frac{360°}{12}=30°$.

Contoh: Tentukan besar sudut yang dibentuk oleh jarum jam dan jarum menit ketika jarum menunjukkan pukul 03.25.

Dengan aturan jarum jam dan jarum menit, saat pukul 03.25 maka jarum pendek menunjukkan bilangan 3,25 pada jam sedangkan jarum panjangnya menunjukkan bilangan 5 pada jam. Kita diminta untuk menentukan besar sudut antara jarum pendek dan jarum panjang. Caranya adalah menghitung besar sudut yang dibentuk selama 5 jam dikurangi besar sudut yang dibentuk selama 3,25 jam.

Karena dalam 1 jam, sebuah jarum jam bergeser sejauh 30° maka besar sudut yang dibentuk selama 5 jam adalah 150° sedangkan sudut yang dibentuk selama 3,25 jam adalah:
$\begin{align} 3 \frac{25}{60} × 30° &= 3×30°+\frac{25}{60} ×30° \\ &= 90°+12,5° \\ &= 102,5° \end{align}$.

Jadi, besar sudut yang terbentuk pada saat pukul 03.25 adalah $150°-102,5°=47,5°$.

Penamaan Sudut

Secara matematis, penamaan sudut diperlukan untuk mempermudah penamaan sudut untuk kajian selanjutnya. Mari kita perhatikan gambar berikut ini.

Dari gambar di atas  $\overrightarrow{BA} dan  $\overrightarrow{BC}$ disebut kaki sudut. Titik B adalah titik sudut. Secara umum, ada dua penamaan sudut, yaitu:

  • Titik B dapat dikatakan sebagai titik sudut B seperti pada gambar. Ingat, penulisannya selalu menggunakan huruf kapital.
  • Sudut yang terbentuk pada gambar di samping dapat juga disimbolkan dengan ∠ABC atau ∠CBA atau ∠B. 

Pada setiap sudut yang terbentuk, harus kita tahu berapa besar derajat sudutnya. Secara manual, kita dapat menggunakan alat ukur sudut yaitu busur. Alat ini dapat membantu kita mengukur suatu sudut yang sudah terbentuk dan membentuk besar sudut yang akan digambar.

Jenis-jenis Sudut

Perlu kita kenalkan bahwa terdapat ukuran sudut standar yang perlu kita ketahui, seperti yang disajikan pada gambar di bawah ini.

  • Sudut Siku-Siku: ukuran sudutnya 90°
  • Sudut Lancip: ukuran sudutnya antara 0° dan 90°
  • Sudut Tumpul: ukuran sudutnya antara 90° dan 180°
  • Sudut Lurus: ukuran sudutnya 180°
  • Sudut Reflek: ukuran sudutnya antara 180° dan 360°
Silahkan lihat daftar tulisan lainnya yang termasuk pada Materi Garis dan Sudut Kelas 7.

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