Question

Yo please help

Triangle D E F is shown. Angle E F D is a right angle. The length of E F is 24 and the length of D F is 7.


Which trigonometric ratios are correct for triangle DEF? Select three options.




sin(D) = StartFraction 24 Over 25 EndFraction



cos(E) = StartFraction 7 Over 25 EndFraction


tan(D) = StartFraction 24 Over 7 EndFraction


sin(E) = StartFraction 7 Over 25 EndFraction


tan(D) = StartFraction 7 Over 24 EndFraction

Answer 1

The answer is A C and D on Edge 2020

Explanation:

Answer 2

Options 1, 3 and 4 are true

Explanation:

The legs EF and DF of the right triangle DEF have lengths of 24 units and 7 units, respectively. By the Pythagorean theorem,

`DE^2=EF^2+DF^2\\ \\DE^2=24^2+7^2\\ \\DE^2=576+49\\ \\DE^2=625\\ \\DE=25\ units`

Find trigonometric functions:

`\sin \angle D=\frac{\text{Opposite leg}}{\text{Hypotenuse}}=(EF)/(DE)=(24)/(25)`

`\cos \angle E=\frac{\text{Adjacent leg}}{\text{Hypotenuse}}=(EF)/(DE)=(24)/(25)`

`\tan \angle D=\frac{\text{Opposite leg}}{\text{Adjacent leg}}=(EF)/(DF)=(24)/(7)`

`\sin \angle E=\frac{\text{Opposite leg}}{\text{Hypotenuse}}=(DF)/(DE)=(7)/(25)`

Thus, options 1, 3 and 4 are true