The value of [tex]x[/tex] is [tex]\boxed{2\sqrt2 }[/tex] and the value of [tex]y[/tex] is [tex]\boxed{2\sqrt 6 }.[/tex]
Further explanation:
The Pythagorean formula can be expressed as,
[tex]\boxed{{H^2} = {P^2} + {B^2}}.[/tex]
Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.
The formula for sin of angle a can be expressed as
[tex]\boxed{\sin a=\frac{P}{H}}[/tex]
The formula for cos of angle a can be expressed as
[tex]\boxed{\cos a=\frac{B}{H}}[/tex]
The formula for tan of angle a can be expressed as
[tex]\boxed{\tan a= \frac{P}{B}}[/tex]
Explanation:
The value of [tex]y[/tex] can be obtained as follows,
[tex]\begin{aligned}\sin {60^ \circ }&=\frac{y}{{4\sqrt 2 }}\\\frac{{\sqrt3 }}{2}&=\frac{y}{{4\sqrt 2 }}\\\frac{{\sqrt3 }}{2} \times 4\sqrt 2&= y\\2\sqrt6\\ \end{aligned}[/tex]
The value of [tex]x[/tex] can be obtained as follows,
[tex]\begin{aligned}\sin {30^ \circ }&= \frac{x}{{4\sqrt 2 }}\\\frac{1}{2}&= \frac{x}{{4\sqrt2 }}\\\frac{{4\sqrt2 }}{2}&= x\\2\sqrt2&= x\\\end{aligned}[/tex]
The value of [tex]x[/tex] is [tex]\boxed{2\sqrt2 }[/tex] and the value of [tex]y[/tex] is [tex]\boxed{2\sqrt 6 }.[/tex]
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Trigonometry
Keywords: value of x, value of y, analyze, diagram, triangle, instructions, Pythagoras theorem.
