Question

Triangle D E F is shown. Angle D E F is a right angle. The length of hypotenuse D F is 5 StartRoot 2 EndRoot and the lengths of sides D E and E F are 5.
Given △DEF, which is not equal to cos(F)?

sin(F).
sin(D).
tan(F).
cos(D)

Answer 1

cos(F) = adjacent/hypotenuse = EF/DF = 5/(5√2) = 1/√2 = √2/2.

Compute the others:
- sin(F) = ED/DF = 5/(5√2) = √2/2 (equal to cos(F))
- sin(D) = EF/DF = 5/(5√2) = √2/2 (equal)
- cos(D) = DE/DF = 5/(5√2) = √2/2 (equal)
- tan(F) = ED/EF = 5/5 = 1 (not equal)

Therefore the one that is not equal to cos(F) is tan(F).