Question

In ADEF, what is sin D, in simplified form?

Answer 1

In simplified form, sin D is;

4/5

Explanation:

The given figure and dimension parameters in the question are;

Triangle ΔDEF is a right triangle

The length of leg
`\overline{EF}` which is opposite side to the reference angle = 20

The length of segment
`\overline{ED}` which is the hypotenuse side of the right triangle ΔDEF = 25

The length of segment
`\overline{DF}` which is adjacent side to the reference angle = 15

By trigonometric ratios, we have;

`sin\angle X = (Opposite \ leg \ length)/(Hypotenuse \ length)`

Therefore, we have;

`sin\angle D = (Opposite \ leg \ length)/(Hypotenuse \ length) = (20)/(25) = (4)/(5)`

∴ In simplified form, sin(D) = 4/5.