Question 100

In ∆XYZ measure of angle Y is 90°. If cosecX = 17/15, and XY = 4cm, then what is the length (in cm) of side YZ?

Solution

Given : $$\cosec X$$ = $$\frac{17}{15}$$

Also, $$\cosec X=\frac{XZ}{YZ}=\frac{17}{15}$$

Let XZ = $$17x$$ cm and YZ = $$15x$$ cm

Thus, in $$\triangle$$ XYZ, => $$(XY)^2=(XZ)^2-(YZ)^2$$

=> $$(XY)^2=(17x)^2-(15x)^2$$

=> $$(XY)^2=289x^2-225x^2=64x^2$$

=> $$XY=\sqrt{64x^2}=8x$$ cm

According to ques, => $$8x=4$$

=> $$x=\frac{4}{8}=\frac{1}{2}$$

$$\therefore$$ YZ = $$15\times\frac{1}{2}=7.5$$ cm

=> Ans - (A)

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