HOTS Zone : Trigonometri Pada Segitiga
Table of Contents
Tipe:
No.
Pada suatu segitiga ABC, sudut C tiga kali besar sudut A dan sudut B dua kali besar sudut A. Berapakah perbandingan (rasio) antara panjang AB dengan BC ?ALTERNATIF PENYELESAIAN
\(\begin{aligned}
\angle A+\angle B+\angle C&=180°\\
\angle A+2\angle A+3\angle A&=180°\\
6\angle A&=180°\\
\angle A&=30°
\end{aligned}\)
\(\begin{aligned} \angle C&=3\angle A\\ &=90° \end{aligned}\)
\(\begin{aligned} \dfrac{AB}{\sin \angle C}&=\dfrac{BC}{\sin\angle A}\\[4pt] \dfrac{AB}{\sin 90°}&=\dfrac{BC}{\sin30°}\\[4pt] \dfrac{AB}1&=\dfrac{BC}{\dfrac12}\\[4pt] \dfrac{AB}{BC}&=\dfrac21 \end{aligned}\)
\(\begin{aligned} \angle C&=3\angle A\\ &=90° \end{aligned}\)
\(\begin{aligned} \dfrac{AB}{\sin \angle C}&=\dfrac{BC}{\sin\angle A}\\[4pt] \dfrac{AB}{\sin 90°}&=\dfrac{BC}{\sin30°}\\[4pt] \dfrac{AB}1&=\dfrac{BC}{\dfrac12}\\[4pt] \dfrac{AB}{BC}&=\dfrac21 \end{aligned}\)
Jadi, perbandingan (rasio) antara panjang AB dengan BC adalah 2:1.
No.
ALTERNATIF PENYELESAIAN
\(\begin{aligned}
\tan\left(\theta+45°\right)&=\dfrac{\tan\theta+\tan45°}{1-\tan\theta\tan45°}\\[4pt]
\dfrac{x+5}3&=\dfrac{\dfrac{x}3+1}{1-\dfrac{x}3\cdot1}\\[4pt]
\dfrac{x+5}3&=\dfrac{x+3}{3-x}\\[4pt]
3x-x^2+15-5x&=3x+9\\
x^2+5x-6&=0\\
(x-1)(x+6)&=0
\end{aligned}\)
x = 1, atau x = −6 (TM)
x = 1, atau x = −6 (TM)
Jadi, x = 1.
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