Question

​For the two right triangles above, explain why a/8=x/12 . ​ ​What ​trigonometric ratio is also equal to the two given ratios?

Answer 1

sin trigonometry ratio

Explanation:

Given

See attachment for triangles

Required

Explain why
`(a)/(8) = (x)/(12)`

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 = (12)/(8)`

`k = 1.5`

(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) = (Opp)/(Hyp)`

This gives:

`sin(30) = (a)/(8)`

In the second triangle:

`sin(30) = (Opp)/(Hyp)`

So:

`sin(30) = (x)/(12)`

By comparison:

`sin(30) = sin(3)`

Hence:

`(a)/(8) = (x)/(12)`