Respuesta :

cerverusdante
We can find m∠BCD like follows: m∠BCD=90°-45°=45°
Now, m∠DBC= 180°-(90°+45°)=45°

Remember that [tex]sin \alpha = \frac{opposite leg}{hypotenuse} [/tex], so [tex]oppositeleg=(hypotenuse)(sin \alpha )[/tex]

We know that hypotenuse= BC= 3in and [tex] \alpha [/tex]=∠DBC)=45°, so replacing the values we get:
[tex]CD=3sin(45)=2.12[/tex]

We can conclude that the segment CD is 2.12 in

The length of CD is determined by using trignometry functions. In the given triangle ABC the length of CD is 2.1213.

Given :

  • [tex]\rm \angle ACB = 90^\circ[/tex]
  • [tex]\rm CD \perp AB[/tex]
  • [tex]\rm \angle ACD = 45^\circ[/tex]
  • [tex]\rm BC = 3[/tex]

In trignometry functions, cosine is the ratio of the base to the hypotenuse. So, from triangle DCB the length of CD can be evaluated as:

[tex]\rm cos45^\circ =\dfrac{CD}{CB}[/tex]

[tex]\rm cos45^\circ =\dfrac{CD}{3}[/tex]

Now, put the value of [tex]\rm cos45^\circ[/tex] which is [tex]1\div \sqrt{2}[/tex] in above equation.

[tex]\rm \dfrac{1}{\sqrt{2} } = \dfrac{CD}{3}[/tex]

[tex]\rm CD = \dfrac{3}{\sqrt{2} }=2.1213[/tex]

In the given triangle ABC the length of CD is 2.1213.

For more information, refer the link given below

https://brainly.com/question/21286835

Otras preguntas