Question 25

ΔDEF is right angled at E. If $$\sin D$$ = $$\frac{15}{17}$$, then what is the value of $$\cot F$$ ?

Solution

Given : $$\sin D$$ = $$\frac{15}{17}$$

Also, $$\sin D=\frac{EF}{DF}=\frac{15}{17}$$

Let EF = 15 cm and DF = 17 cm

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

=> $$(DE)^2=(17)^2-(15)^2$$

=> $$(DE)^2=289-225=64$$

=> $$DE=\sqrt{64}=8$$ cm

To find : $$\cot F=\frac{EF}{DE}$$

= $$\frac{15}{8}$$

=> Ans - (C)

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