Answer:
sin ∠FDE is 12/13
Step-by-step explanation:
The trigonometric ratios will be used to find the value of sin∠FDE
In the given triangle, according to angle FDE
Base = DE = 5
Hypotenuse = DF = 13
Perpendicular = EF = ?
sin ∠FDE = [tex]\frac{perpendicular}{Hypotenuse} = \frac{EF}{DF}[/tex]
We have to find the length of DF first
Pythagoras theorem will be used as the given triangle is a right angled triangle
[tex](Hypotenuse)^2 = (Base)^2+(perpendicular)^2\\(DF)^2 = (DE)^2+(EF)^2\\(13)^2 = (5)^2 + EF^2\\169 = 25+EF^2\\EF^2 = 169-25\\EF^2 = 144\\\sqrt{EF^2} = \sqrt{144}\\EF = 12[/tex]
So,
sin ∠FDE = EF/DF
sin ∠FDE = 12/13
Hence,
sin ∠FDE is 12/13
