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

Answer:

sin trigonometry ratio

Step-by-step explanation:

Given

See attachment for triangles

Required

Explain why $\frac{a}{8} = \frac{x}{12}$

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

$k = \frac{12}{8}$

$k = 1.5$

(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:

$sin(30) = \frac{Opp}{Hyp}$

This gives:

$sin(30) = \frac{a}{8}$

In the second triangle:

$sin(30) = \frac{Opp}{Hyp}$

So:

$sin(30) = \frac{x}{12}$

By comparison:

$sin(30) = sin(3)$

Hence:

$\frac{a}{8} = \frac{x}{12}$