7 .02
8 .21
9 .014
These are the correct answer
Answer:
sin trigonometry ratio
Step-by-step explanation:
Given
See attachment for triangles
Required
Explain why ![\frac{a}{8} = \frac{x}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B8%7D%20%3D%20%5Cfrac%7Bx%7D%7B12%7D)
From the attached diagram, both triangles are similar triangles because
(1) the second triangle is a dilation of the first triangle by a ratio of 1.5
i.e
![k = \frac{12}{8}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B12%7D%7B8%7D)
![k = 1.5](https://tex.z-dn.net/?f=k%20%3D%201.5)
(2) They have angle 30 degrees, and have their right angles located at the same point
In the first triangle, the sine of 30 degrees is represented as:
![sin(30) = \frac{Opp}{Hyp}](https://tex.z-dn.net/?f=sin%2830%29%20%3D%20%5Cfrac%7BOpp%7D%7BHyp%7D)
This gives:
![sin(30) = \frac{a}{8}](https://tex.z-dn.net/?f=sin%2830%29%20%3D%20%5Cfrac%7Ba%7D%7B8%7D)
In the second triangle:
![sin(30) = \frac{Opp}{Hyp}](https://tex.z-dn.net/?f=sin%2830%29%20%3D%20%5Cfrac%7BOpp%7D%7BHyp%7D)
So:
![sin(30) = \frac{x}{12}](https://tex.z-dn.net/?f=sin%2830%29%20%3D%20%5Cfrac%7Bx%7D%7B12%7D)
By comparison:
![sin(30) = sin(3)](https://tex.z-dn.net/?f=sin%2830%29%20%3D%20sin%283%29)
Hence:
![\frac{a}{8} = \frac{x}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B8%7D%20%3D%20%5Cfrac%7Bx%7D%7B12%7D)
Answer:
6^5
Step-by-step explanation:
Six to the power five is written as factorized form is 6^5 or 6*6*6*6*6
Use the same to solve the rest of the problems. Hope this helps:)