Question 25
In ΔDEF measure of angle E is $$90^\circ$$. If $$cos D = \frac{5}{13}$$, and DE = 1cm, then what is the length (in cm) of side EF?
Solution
Given : DE = 1 cm and cos D = $$\frac{5}{13}$$
To find : EF = ?
Solution : In right $$\triangle$$ DEF,
=> $$cos(D)=\frac{DE}{DF}$$
=> $$\frac{5}{13}=\frac{1}{DF}$$
=> $$DF=\frac{13}{5}\times1=2.6$$ cm
$$\therefore$$ $$(DF)^2=(DE)^2+(EF)^2$$
=> $$(EF)^2=(2.6)^2-(1)^2$$
=> $$(EF)^2=6.76-1=5.76$$
=> $$EF=\sqrt{5.76}=2.4$$ cm
=> Ans - (B)
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