1.
[tex]a = 18cm\\\alpha = 30\\sin30=\frac{18}{c}\\\frac12=\frac{18}c\\c=2*18=36\\cos30=\frac{b}{36}\\\frac{\sqrt3}2=\frac{b}{36}\\b=\frac{36\sqrt3}{2}\\b=18\sqrt3[/tex]
2.
[tex]tg\alpha = \frac49\\tg\alpha = \frac{sin\alpha}{cos\alpha}\\\frac49 = \frac{sin\alpha}{cos\alpha}\\4cos\alpha=9sin\alpha\\cos\alpha = \frac94sin\alpha\\sin^2\alpha+cos^2\alpha=1\\sin^2\alpha+(\frac94sin\alpha)^2 = 1\\sin^2\alpha+\frac{81}{16}sin^2\alpha=1\\\frac{16}{16}sin^2\alpha+\frac{81}{16}sin^2\alpha=1\\\frac{97}{16}sin^2\alpha=1 /*16\\97sin^2\alpha=16 /:97\\sin^2\alpha = \frac{16}{97}\\sin\alpha=\frac{4}{\sqrt{97}} = \frac{4\sqrt{97}}{97}\\sin^2\alpha+cos^2\alpha=1\\[/tex]
[tex]\frac{16}{97}+cos^2\alpha=1\\cos^2\alpha=1-\frac{16}{97}\\cos^2\alpha=\frac{81}{97}\\cos\alpha=\frac{9}{\sqrt{97}} = \frac{9\sqrt{97}}{97}[/tex]
3.
[tex]a) \\\sqrt[4]2*\sqrt[4]8=\sqrt[4]{2*8}=\sqrt[4]{16}=2\\b) \\\sqrt[3]{343}:64 = \sqrt[3]{7*7*7}:64=7:64=\frac7{64}\\c) \\\sqrt[3]{64}*216=4*216=864\\d) \\\sqrt[5]{27}*\sqrt[5]{9}=\sqrt[5]{243}=\sqrt[5]{3*3*3*3*3}=3\\e) (\frac{1}{2})^2*(\frac18)^2=(\frac12)^2*[(\frac12)^3]^2=(\frac12)^2*(\frac12)^6=(\frac12)^8=\frac1{256}[/tex]