Question 25

ΔDEF is right angled at E. If cotD = 5/12, then what is the value of sinF ?

Solution

Given : $$\cot D$$ = $$\frac{5}{12}$$

Also, $$\cot D=\frac{DE}{EF}=\frac{5}{12}$$

Let DE = 5 cm and EF = 12 cm

Thus, in $$\triangle$$ DEF, => $$(DF)^2=(DE)^2+(EF)^2$$

=> $$(DF)^2=(5)^2+(12)^2$$

=> $$(DF)^2=25+144=169$$

=> $$DF=\sqrt{169}=13$$ cm

To find : $$\sin F=\frac{DE}{DF}$$

= $$\frac{5}{13}$$

=> Ans - (C)

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