Question

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 correct options are 1, 3 and 4.

Explanation:

Consider the below figure attached with this question.

From the figure it is clear that DF = 7 units and EF = 24 units.

According to the Pythagoras theorem, in a right angled triangle

`hypotenuse^2=perpendicular^2+base^2`

Using Pythagoras theorem, we get

`D E^2=E F^2+D F^2`

`D E^2=24^2+7^2`

`D E^2=625`

Taking square root on both sides.

`D E=25`

In a right angle triangle

`\sin \theta = (opposite)/(hypotenuse)`

`\cos \theta = (adjacent)/(hypotenuse)`

`\tan \theta = (opposite)/(adjacent)`

Using these ratio we get

`\sin (D)=(EF)/(DE)=(24)/(25)`

`\cos (E)=(EF)/(DE)=(24)/(25)`

`\tan (D)=(EF)/(DF)=(24)/(7)`

`\sin (E)=(DF)/(DE)=(7)/(25)`

Therefore, the correct options are 1, 3 and 4.