Question

given △def, which is not equal to cos(f)?
○ sin(f).
○ sin(d).
○ tan(f).
○ cos(d).
(△def is a right triangle with right angle at e, de = 5, ef = 5, df = 5√2)

Explanation:

Step1: Identify triangle type

$\triangle DEF$ is isosceles right triangle (legs $DE = EF = 5$, hypotenuse $DF = 5\sqrt{2}$), so $\angle D=\angle F = 45^\circ$.

Step2: Calculate $\cos(F)$

$\cos(F)=\cos(45^\circ)=\frac{\sqrt{2}}{2}$.

Step3: Evaluate other trigonometric functions

• $\sin(F)=\sin(45^\circ)=\frac{\sqrt{2}}{2}$
• $\sin(D)=\sin(45^\circ)=\frac{\sqrt{2}}{2}$
• $\tan(F)=\tan(45^\circ)=1$
• $\cos(D)=\cos(45^\circ)=\frac{\sqrt{2}}{2}$

Answer:

$\tan(F)$