Question

Kellie also says this is a 30-60-90 triangle because the sum of is 6√/2.

Eddie says this is a 30-60-90 triangle because the sum of ZN and ZM is the
same as the measure of ZMOP. So if the measure of NO is 4√6, MN is 12√2
, and MO is 8√6.
Which student is accurate and why?

Answer 1

The student who is accurate is Eddie.

Eddie correctly identifies the triangle as a 30-60-90 triangle. In a 30-60-90 triangle, the sides are in the ratio 1:√3:2. Let's see how Eddie's reasoning matches this ratio.

First, let's assign the given measurements to the sides of the triangle:

- NO = 4√6

- MN = 12√2

- MO = 8√6

Now, let's compare the lengths of the sides:

- NO/MN = (4√6)/(12√2) = (√6)/(3√2) = (√6)/(√(3*2)) = (√6)/(√6) = 1

- MN/MO = (12√2)/(8√6) = (√2)/(√6) = (√2)/(√(2*3)) = (√2)/(√2√3) = 1/√3 = (√3)/(√3*√3) = (√3)/(√9) = (√3)/3

- NO/MO = (4√6)/(8√6) = 1/2

We can see that NO/MN = 1, MN/MO = (√3)/3, and NO/MO = 1/2. These ratios match the ratios in a 30-60-90 triangle, where the sides are in the ratio 1:√3:2.

Therefore, Eddie's reasoning is correct, and he accurately identifies the triangle as a 30-60-90 triangle based on the ratio of the sides.

Have a great day/week

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