Soalan 3:
Tentukan panjang sisi q untuk setiap segi tiga bersudut tegak berikut.
Penyelesaian:
$$ \sin =\frac{\text { sisi bertentangan }(0)}{\text { hipotenus }(\mathrm{H})} $$
(a)
$$ \begin{aligned} &\text { Diberi } \sin \angle Q R P=\frac{1}{3}\\ &\begin{aligned} \frac{q}{9} & =\frac{1}{3} \\ q & =\frac{1}{3} \times 9 \\ & =3 \mathrm{~m} \end{aligned} \end{aligned} $$
(b)
$$ \begin{aligned} &\text { Diberi } \sin \angle L K M=\frac{7}{8}\\ &\begin{aligned} \frac{q}{24} & =\frac{7}{8} \\ q & =\frac{7}{8} \times 24 \\ & =21 \mathrm{~m} \end{aligned} \end{aligned} $$
(c)
$$ \begin{aligned} \sin \angle A C B & =\frac{2}{5} \\ \frac{10}{q} & =\frac{2}{5} \\ 50 & =2 q \\ 2 q & =50 \\ q & =\frac{50}{2} \\ & =25 \mathrm{~mm} \end{aligned} $$
Tentukan panjang sisi q untuk setiap segi tiga bersudut tegak berikut.
Penyelesaian:
$$ \sin =\frac{\text { sisi bertentangan }(0)}{\text { hipotenus }(\mathrm{H})} $$
(a)
$$ \begin{aligned} &\text { Diberi } \sin \angle Q R P=\frac{1}{3}\\ &\begin{aligned} \frac{q}{9} & =\frac{1}{3} \\ q & =\frac{1}{3} \times 9 \\ & =3 \mathrm{~m} \end{aligned} \end{aligned} $$
(b)
$$ \begin{aligned} &\text { Diberi } \sin \angle L K M=\frac{7}{8}\\ &\begin{aligned} \frac{q}{24} & =\frac{7}{8} \\ q & =\frac{7}{8} \times 24 \\ & =21 \mathrm{~m} \end{aligned} \end{aligned} $$
(c)
$$ \begin{aligned} \sin \angle A C B & =\frac{2}{5} \\ \frac{10}{q} & =\frac{2}{5} \\ 50 & =2 q \\ 2 q & =50 \\ q & =\frac{50}{2} \\ & =25 \mathrm{~mm} \end{aligned} $$
Soalan 4:
Tentukan panjang sisi z untuk setiap segi tiga bersudut tegak berikut.
Penyelesaian:
$$ \operatorname{kos} \theta=\frac{\operatorname{sisi} \text { bersebelahan }(\mathrm{A})}{\operatorname{hipotenus}(\mathrm{H})} $$
(a)
$$ \begin{aligned} \operatorname{kos} \angle S R T & =\frac{5}{7} \\ \frac{z}{14} & =\frac{5}{7} \\ z & =\frac{5}{7} \times 14 \\ & =10 \mathrm{~cm} \end{aligned} $$
(b)
$$ \begin{aligned} \operatorname{kos} \angle H J I & =\frac{3}{8} \\ \frac{z}{40} & =\frac{3}{8} \\ z & =\frac{3}{8} \times 40 \\ & =15 \mathrm{~cm} \end{aligned} $$
(c)
$$ \begin{aligned} \operatorname{kos} \angle D F E & =0.4 \\ \frac{12}{z} & =0.4 \\ z & =\frac{12}{0.4} \\ & =30 \mathrm{~mm} \end{aligned} $$
Tentukan panjang sisi z untuk setiap segi tiga bersudut tegak berikut.
Penyelesaian:
$$ \operatorname{kos} \theta=\frac{\operatorname{sisi} \text { bersebelahan }(\mathrm{A})}{\operatorname{hipotenus}(\mathrm{H})} $$
(a)
$$ \begin{aligned} \operatorname{kos} \angle S R T & =\frac{5}{7} \\ \frac{z}{14} & =\frac{5}{7} \\ z & =\frac{5}{7} \times 14 \\ & =10 \mathrm{~cm} \end{aligned} $$
(b)
$$ \begin{aligned} \operatorname{kos} \angle H J I & =\frac{3}{8} \\ \frac{z}{40} & =\frac{3}{8} \\ z & =\frac{3}{8} \times 40 \\ & =15 \mathrm{~cm} \end{aligned} $$
(c)
$$ \begin{aligned} \operatorname{kos} \angle D F E & =0.4 \\ \frac{12}{z} & =0.4 \\ z & =\frac{12}{0.4} \\ & =30 \mathrm{~mm} \end{aligned} $$
Soalan 5:
Hitung nilai x bagi setiap segi tiga bersudut tegak berikut.
Penyelesaian:
$$ \tan \theta=\frac{\text { sisi bertentangan }(0)}{\text { sisi bersebelahan }(\mathrm{A})} $$
(a)
$$ \begin{aligned} \tan \angle B A C & =0.9 \\ \frac{x}{20} & =0.9 \\ x & =0.9 \times 20 \\ & =18 \mathrm{~cm} \end{aligned} $$
(b)
$$ \begin{aligned} \tan \angle P R Q & =\frac{3}{4} \\ \frac{12}{Q R} & =\frac{3}{4} \\ 12 \times \frac{4}{3} & =Q R \\ Q R & =16 \mathrm{~cm} \end{aligned} $$
$$ \begin{aligned} x^2 & =P Q^2+Q R^2 \\ x & =\sqrt{12^2+16^2} \\ & =\sqrt{400} \\ & =20 \mathrm{~cm} \end{aligned} $$
(c)
$$ \begin{aligned} \tan \angle L K M & =\frac{10}{3} \\ \frac{30}{x} & =\frac{10}{3} \\ 30 \times \frac{3}{10} & =x \\ 9 & =x \\ x & =9 \mathrm{~mm} \end{aligned} $$
Hitung nilai x bagi setiap segi tiga bersudut tegak berikut.
Penyelesaian:
$$ \tan \theta=\frac{\text { sisi bertentangan }(0)}{\text { sisi bersebelahan }(\mathrm{A})} $$
(a)
$$ \begin{aligned} \tan \angle B A C & =0.9 \\ \frac{x}{20} & =0.9 \\ x & =0.9 \times 20 \\ & =18 \mathrm{~cm} \end{aligned} $$
(b)
$$ \begin{aligned} \tan \angle P R Q & =\frac{3}{4} \\ \frac{12}{Q R} & =\frac{3}{4} \\ 12 \times \frac{4}{3} & =Q R \\ Q R & =16 \mathrm{~cm} \end{aligned} $$
$$ \begin{aligned} x^2 & =P Q^2+Q R^2 \\ x & =\sqrt{12^2+16^2} \\ & =\sqrt{400} \\ & =20 \mathrm{~cm} \end{aligned} $$
(c)
$$ \begin{aligned} \tan \angle L K M & =\frac{10}{3} \\ \frac{30}{x} & =\frac{10}{3} \\ 30 \times \frac{3}{10} & =x \\ 9 & =x \\ x & =9 \mathrm{~mm} \end{aligned} $$