Option a: Sin F equal to [tex]\frac{9}{41}[/tex]
Option e: Cos G equal to [tex]\frac{9}{41}[/tex]
Explanation:
Option a : Sin F
Let us determine the value of Sin F from the right triangle.
The formula for Sin F is [tex]\sin F=\frac{o p p}{h y p}[/tex]
Thus, substituting the values, we get,
[tex]\begin{aligned}\sin F &=\frac{o p p}{h y p} \\&=\frac{H G}{F G} \\&=\frac{9}{41}\end{aligned}[/tex]
Hence, [tex]\begin{aligned}\sin F &=\frac{9}{41}\end{aligned}[/tex] which is equal to [tex]\frac{9}{41}[/tex]
Hence, Option a is the correct answer.
Option b : Cos F
The formula to determine the value of Cos F is [tex]\cos F=\frac{a d j}{h y p}[/tex]
Thus, substituting the values, we get,
[tex]\begin{aligned}\cos F &=\frac{a d j}{h y p} \\&=\frac{F H}{F G} \\&=\frac{40}{41}\end{aligned}[/tex]
Hence, [tex]\begin{aligned}\cos F &=\frac{40}{41}\end{aligned}[/tex] which is not equal to [tex]\frac{9}{41}[/tex]
Hence, Option b is not the correct answer.
Option c: tan F
The formula to determine the value of tan F is [tex]\tan F=\frac{o p p}{a d j}[/tex]
Thus, substituting the values, we get,
[tex]\begin{aligned}\tan F &=\frac{o p p}{a d j} \\&=\frac{F H}{H G} \\&=\frac{9}{40}\end{aligned}[/tex]
Hence, [tex]\begin{aligned}\tan F &=\frac{9}{40}\end{aligned}[/tex] which is not equal to [tex]\frac{9}{41}[/tex]
Hence, Option c is not the correct answer.
Option d : Sin G
The formula to determine the value of Sin G is [tex]\sin G=\frac{o p p}{h y p}[/tex]
Thus, substituting the values, we get,
[tex]\begin{aligned}\sin G &=\frac{o p p}{h y p} \\&=\frac{FH }{F G} \\&=\frac{40}{41}\end{aligned}[/tex]
Hence, [tex]\begin{aligned}\sin G &=\frac{40}{41}\end{aligned}[/tex] which is not equal to [tex]\frac{9}{41}[/tex]
Hence, Option d is not the correct answer.
Option e : Cos G
The formula to determine the value of Cos G is [tex]\cos G=\frac{a d j}{h y p}[/tex]
Thus, substituting the values, we get,
[tex]\begin{aligned}\cos G &=\frac{a d j}{h y p} \\&=\frac{HG}{F G} \\&=\frac{9}{41}\end{aligned}[/tex]
Hence, [tex]\begin{aligned}\cos F &=\frac{40}{41}\end{aligned}[/tex] which is equal to [tex]\frac{9}{41}[/tex]
Hence, Option e is the correct answer.
Option f : tan G
The formula to determine the value of tan G is [tex]\tan G=\frac{o p p}{a d j}[/tex]
Thus, substituting the values, we get,
[tex]\begin{aligned}\tan G &=\frac{o p p}{a d j} \\&=\frac{F H}{H G} \\&=\frac{40}{9}\end{aligned}[/tex]
Hence, [tex]\begin{aligned}\tan G &=\frac{40}{9}\end{aligned}[/tex] which is not equal to [tex]\frac{9}{41}[/tex]
Hence, Option f is not the correct answer.
Thus, the expression which is equal to [tex]\frac{9}{41}[/tex] is Sin F and Cos G
