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Alexxx [7]
2 years ago
7

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

Mathematics
1 answer:
frutty [35]2 years ago
8 0

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}

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