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

Question

asked Dec 17, 2019 56.9k views

2 Answers

Matt Thomas · Answer 1 · 2019-12-23T08:45:16+0000

Answer: The correct option is tan(F).

Step-by-step 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√(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.

$\cos (F)=(Base)/(Hypotenuse) =(5)/(5√(2)) =(1)/(√(2))$

The value of cos(F) is
(1)/(√(2)) .

$\sin (F)=(Perpendicular)/(Hypotenuse) =(5)/(5√(2)) =(1)/(√(2))$

The value of sin(F) is
(1)/(√(2)) .

$\sin (D)=(Perpendicular)/(Hypotenuse) =(5)/(5√(2)) =(1)/(√(2))$

The value of sin(D) is
(1)/(√(2)) .

$\tan (F)=(Perpendicular)/(Base)=(5)/(5) =1$

The value of tan(F) is 1. Which is not equal to
(1)/(√(2)) .

$\cos (D)=(Base)/(Hypotenuse) =(5)/(5√(2)) =(1)/(√(2))$

The value of cos(D) is
(1)/(√(2)) .

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