Question 25

In ΔXYZ measure of angle Y is 90°. If cosecX = 13/12, and XY = 1cm, then what is the length ( in cm ) of side YZ?

Solution

Given : $$\cosec X$$ = $$\frac{13}{12}$$

Also, $$\cosec X=\frac{XZ}{YZ}=\frac{13}{12}$$

Let XZ = $$13x$$ cm and YZ = $$12x$$ cm

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

=> $$(XY)^2=(13x)^2-(12x)^2$$

=> $$(XY)^2=169x^2-144x^2=25x^2$$

=> $$XY=\sqrt{25x^2}=5x$$ cm

According to ques, => $$5x=1$$

=> $$x=\frac{1}{5}$$

$$\therefore$$ YZ = $$12\times\frac{1}{5}=2.4$$ cm

=> Ans - (C)

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