Question

Find the values of x and y

Answer 1

You can use a tangent:

$tangent=\dfrac{opposite}{adjacent}$

We have opposite = 17 and adjacent = x.

$\tan30^o=\dfrac{\sqrt3}{3}$

substitute:

$\dfrac{17}{x}=\dfrac{\sqrt3}{3}$       cross multiply

$x\sqrt3=(3)(17)$     multiply both sides by √3

$x(\sqrt3)(\sqrt3)=51\sqrt3$

$3x=51\sqrt3$      divide both sides by 3

$x=17\sqrt3$

Use the Pythagorean theorem:

$y^2=(17\sqrt3)^2+17^2\\\\y^2=289(\sqrt3)^2+289\\\\y^2=289\cdot3+289\\\\y^2=867+289\\\\y^2=1156\to y=\sqrt{1156}\\\\y=34$

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Other method.

$30^o-60^o-90^o$ triangle.

The sides are in the ratio $1:2:\sqrt3\to17:y:x$

Therefore

$17:(2\cdot17):(17\sqrt3)\to17:34:17\sqrt3\to x=34,\ y=17\sqrt3$