Question

Given △DEF, which is not equal to cos(F)? sin(F). sin(D). tan(F). cos(D)

Answer 1

the answer is tan(F)

Answer 2

Answer: The correct option is tan(F).

Explanation:

In the given figure the triangle is a right angle triangle because $\angle E=90^{\circ}$.

It is also given that $DE=EF=5$ and $DF=5\sqrt{2}$.

Since it is an isosceles right angle triangle, therefore the value of perpendicular and base is same for both angles D and F, which is 5.

$\cos (F)=\frac{Base}{Hypotenuse} =\frac{5}{5\sqrt{2}} =\frac{1}{\sqrt{2}}$

The value of cos(F) is $\frac{1}{\sqrt{2}}$.

$\sin (F)=\frac{Perpendicular}{Hypotenuse} =\frac{5}{5\sqrt{2}} =\frac{1}{\sqrt{2}}$

The value of sin(F) is $\frac{1}{\sqrt{2}}$.

$\sin (D)=\frac{Perpendicular}{Hypotenuse} =\frac{5}{5\sqrt{2}} =\frac{1}{\sqrt{2}}$

The value of sin(D) is $\frac{1}{\sqrt{2}}$.

$\tan (F)=\frac{Perpendicular}{Base}=\frac{5}{5} =1$

The value of tan(F) is 1. Which is not equal to $\frac{1}{\sqrt{2}}$.

$\cos (D)=\frac{Base}{Hypotenuse} =\frac{5}{5\sqrt{2}} =\frac{1}{\sqrt{2}}$

The value of cos(D) is $\frac{1}{\sqrt{2}}$.

Therefore, the value of tan(F) is not equal to the value of cos(F), so the correct option is third.