5.3.3 Buku Teks (Cabaran Dinamis)

Mahir Diri

Soalan 1:
Hitung nilai operasi berikut tanpa menggunakan kalkulator.
(a) 8 sin 60° – 3 tan 60°
(b) (tan 30°)(2 kos 30°) + 6 sin 30°
(c) (8 kos 45°)(sin 60°) + (8 sin 45°)(kos 30°)

Penyelesaian:
(a)
$\begin{array}{l}8\sin {60}^o-3\tan {60}^o\\ ={\cancel{8}}^4\left(\frac{\sqrt{3}}{\cancel{2}}\right)-3\left(\sqrt{3}\right)\\ =\sqrt{3}\end{array}$

(b)
$\begin{array}{l}\left(\tan {30}^o\right)\left(2\text{kos}{30}^o\right)+6\sin {30}^o\\ =\left(\frac{1}{\cancel{\sqrt{3}}}\right)\left[\cancel{2}\left(\frac{\cancel{\sqrt{3}}}{\cancel{2}}\right)\right]+{\cancel{6}}^3\left(\frac{1}{\cancel{2}}\right)\\ =4\end{array}$

(c)
$\begin{array}{l}\left(8kos{45}^o\right)\left(\sin {60}^o\right)+\left(8\sin {45}^o\right)\left(kos{30}^o\right)\\ ={\cancel{8}}^4\left(\frac{1}{\sqrt{2}}\right)\left(\frac{\sqrt{3}}{\cancel{2}}\right)+{\cancel{8}}^4\left(\frac{1}{\sqrt{2}}\right)\left(\frac{\sqrt{3}}{\cancel{2}}\right)\\ =4\sqrt{\frac{3}{2}}+4\sqrt{\frac{3}{2}}\\ =8\sqrt{\frac{3+3}{2+2}}=8\sqrt{\frac{6}{4}}\\ ={\cancel{8}}^4\frac{\sqrt{6}}{\cancel{2}}\\ =4\sqrt{6}\end{array}$

Soalan 2:


Rajah menunjukkan segi tiga bersudut tegak PRS.
PQR ialah garis lurus. Diberi bahawa QR = RS = 18 cm dan $\tan \theta =\frac{3}{5}.$ Hitung
(a) panjang PQ, dalam cm
(b) panjang PS, dalam cm, betul kepada integer terdekat
(c) nilai y

Penyelesaian:
(a)
$\begin{array}{l}\tan \theta =\frac{SR}{PR}\\ \frac{SR}{PR}=\frac{3}{5}\\ \frac{18}{PR}=\frac{3}{5}\\ PR=\frac{5}{3}\times 18\\ PR=30\\ \\ PQ=PR-18\\ =30-18\\ =12\text{ cm}\end{array}$

(b)
$\begin{array}{l}PS=\sqrt{P{R}^2+R{S}^2}\\ PS=\sqrt{{30}^2+{18}^2}\\ PS=\sqrt{900+324}\\ PS=\sqrt{1224}\\ PS=34.99\\ PS=35\text{ cm }\left(\text{integer terdekat}\right)\end{array}$

(c)
$\begin{array}{l}\tan y=\frac{18}{18}\\ \tan y=1\\ y={\tan }^{-1}1\\ y={45}^o\end{array}$