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------------------------------------------------ In ΔDEF, where ∠F = 90°, FE = 39, ED = 89, and DF = 80, what ratio represents the sine of ∠D?

Answer :

Answer:Sin of ∠D = 39/89

Step-by-step explanation:

The diagram of the right angle DEF is shown in the attached photo.

To determine the ratio representing the sine of ∠D, we would apply the sine trigonometric ratio. It is expressed as

Sin# = opposite side/hypotenuse

Looking at the triangle

Opposite side = 39

Hypotenuse = 89

# = ∠D

Therefore

Sin of ∠D = 39/89

Final answer:

The sine of ∠D in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. So, in ΔDEF, sine of ∠D is FE/ED = 39/89.

Explanation:

In trigonometry, the sine of an angle in a right triangle is defined as the ratio of the length of the side that is opposite that angle, to the length of the hypotenuse. Considering this, the ratio representing the sine of ∠D in ΔDEF would be the length of side FE (opposite ∠D) divided by the length of side ED (the hypotenuse in ΔDEF because ∠F is a right angle and ED lies opposite to it).

Therefore, the ratio representing the sine of ∠D is FE/ED = 39/89.

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