Question 25

In ΔUVW measure of angle V is 90°. If cosecU = 13/12, and UV = 2.5cm, then what is the length (in cm) of side VW?

Solution

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

Also, $$\cosec U=\frac{UW}{VW}=\frac{13}{12}$$

Let UW = $$13x$$ cm and VW = $$12x$$ cm

Thus, in $$\triangle$$ UVW, => $$(UV)^2=(UW)^2-(VW)^2$$

=> $$(UV)^2=(13X)^2-(12X)^2$$

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

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

According to ques, => $$5x=2.5$$

=> $$x=\frac{2.5}{5}=\frac{1}{2}$$

$$\therefore$$ VW = $$12\times\frac{1}{2}=6$$ cm

=> Ans - (B)

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