Answer:
The statement would best represent the value of a is a = [tex]\frac{6}{tan(38)}[/tex] ⇒ c
Step-by-step explanation:
In the right angle triangle, we can use the trigonometry ratios to find the missing sides or angles
- sin β = [tex]\frac{opposite}{hypotenuse}[/tex]
- cos β = [tex]\frac{adjacent}{hypotenuse}[/tex]
- tan β = [tex]\frac{opposite}{adjacent}[/tex]
In the given right triangle
∵ There measure of an acute angle is 38°
∵ The adjacent side to this angle is a
∵ The opposite side to this angle is 6
→ We will use the tangent ratio because we have the opposite and
adjacent sides of the given angle
∴ tan(38°) = [tex]\frac{6}{a}[/tex]
→ Multiply both sides by a to cancel the denominator in the right side
∴ a · tan(38°) = 6
→ Divide both sides by tan(38°) to find a
∴ a = [tex]\frac{6}{tan(38)}[/tex]
∴ The statement would best represent the value of a is a = [tex]\frac{6}{tan(38)}[/tex]
