The value of x is [tex]\boxed{4{\text{ units}}}.[/tex] Option (B) is correct.
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]
Given:
The options are as follows,
(A).[tex]\frac{{4\sqrt 2 }}{2}[/tex]
(B).4
(C).[tex]4\sqrt 2[/tex]
(D).[tex]4\sqrt 3[/tex]
Explanation:
The hypotenuse of the triangle is [tex]4\sqrt 2.[/tex]
The perpendicular of the triangle is x.
Consider the base of triangles as y.
The value of x can be calculated as follows,
[tex]\sin {45^ \circ }=\dfrac{x}{{4\sqrt 2 }}[/tex]
The value of [tex]\sin {45^\circ } \:{\text{is}\:\dfrac{1}{{\sqrt 2 }}.[/tex]
[tex]\begin{aligned}\frac{1}{{\sqrt 2 }}&=\frac{x}{{4\sqrt 2 }}\\\frac{{4\sqrt 2 }}{{\sqrt 2 }}&= x\\4&=x\\\end{aligned}[/tex]
The value of x is [tex]\boxed{4{\text{ units}}}.[/tex] Option (B) is correct.
Option (A) is not correct.
Option (B) is correct.
Option (C) is not correct.
Option (D) is not correct.
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: perpendicular bisectors, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions.
