Question

Analyze the diagram below and complete the instructions that follow.

Answer 1

When you have a right triangle with 45 degrees as shown
 the hypotenuse would be the length of the side times sqrt(2)

so the side length for this would be 4

Answer 2

The value of x is $\boxed{4{\text{ units}}}.$ Option (B) is correct.

Further explanation:

The Pythagorean formula can be expressed as,

$\boxed{{H^2} = {P^2} + {B^2}}.$

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

$\boxed{\sin a = \frac{P}{H}}$

The formula for cos of angle a can be expressed as

$\boxed{\cos a = \frac{B}{H}}$

The formula for tan of angle a can be expressed as

$\boxed{\tan a = \frac{P}{B}}$

Given:

The options are as follows,

(A).$\frac{{4\sqrt 2 }}{2}$

(B).4

(C).$4\sqrt 2$

(D).$4\sqrt 3$

Explanation:

The hypotenuse of the triangle is $4\sqrt 2.$

The perpendicular of the triangle is x.

Consider the base of triangles as y.

The value of x can be calculated as follows,

$\sin {45^ \circ }=\dfrac{x}{{4\sqrt 2 }}$

The value of $\sin {45^\circ } \:{\text{is}\:\dfrac{1}{{\sqrt 2 }}.$

$\begin{aligned}\frac{1}{{\sqrt 2 }}&=\frac{x}{{4\sqrt 2 }}\\\frac{{4\sqrt 2 }}{{\sqrt 2 }}&= x\\4&=x\\\end{aligned}$

The value of x is $\boxed{4{\text{ units}}}.$ 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 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.