Respuesta :
The length of the other skating surface, AD is [tex]4\sqrt{2}[/tex].
Given that,
Isaiah sketches a model of a skateboard ramp.
The model has two surfaces on which to skate, represented by sides AB and AD in the diagram.
The steepest side of the model, AB, measures 4 inches.
We have to determine,
What is the length of the other skating surface, AD?
According to the question,
The steepest side of the model, AB, measures 4 inches.
From ΔABC, using trigonometry.
[tex]\rm Sin\theta = \dfrac{AC}{AB}[/tex]
Where [tex]\rm \theta = 45 \ degree[/tex] and AB = 4,
Then,
[tex]\rm Sin\theta = \dfrac{AC}{AB}\\\\\rm Sin45= \dfrac{AC}{4}\\\\\dfrac{1}{\sqrt{2}} = \dfrac{AC}{4}\\\\\\AC = \dfrac{4}{\sqrt{2}}\\\\AC = \dfrac{2 \times \sqrt{2} \times \sqrt{2} }{\sqrt{2}}\\\\AC ={2 \ \sqrt{2} \\[/tex]
And in the triangle ΔACD,
[tex]\rm Sin\theta = \dfrac{AC}{AD}[/tex]
Where [tex]\rm \theta = 30 \ degree[/tex] and [tex]AC = 2\sqrt{2}[/tex]
Then,
[tex]\rm Sin\theta = \dfrac{AC}{AD}\\\\\rm Sin30= \dfrac{2\sqrt{2} }{AD}\\\\\dfrac{1}{2}} = \dfrac{2\sqrt{2} }{AD}\\\\\\AD = 4\sqrt{2}[/tex]
The length of AD will be [tex]4\sqrt{2}[/tex].
Hence, The length of the other skating surface, AD is [tex]4\sqrt{2}[/tex].
For more details about Trigonometry refer to the link given below.
https://brainly.com/question/743546
Answer:
B
Step-by-step explanation:
Just simplifying what the guy above put lol.
