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Andrei [34K]
3 years ago
11

Fifteen less than twice a number is less than or equal to -23

Mathematics
1 answer:
lutik1710 [3]3 years ago
5 0
I would think the answer is -16 

but that's is what i think

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Find the missing side lengths leave your answer as a racials simplest form
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Step-by-step explanation:

Hi there!

We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14

We need to find the lengths of m and n

Firstly, let's find the measure of the other acute angle

The acute angles in a right triangle are complementary, meaning they add up to 90 degrees

Let's make the measure of the unknown acute angle x

So x+60°=90°

Subtract 60 from both sides

x=30°

So the measure of the other acute angle is 30 degrees

This makes the right triangle a special kind of right triangle, a 30°-60°-90°  triangle

In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is \frac{a}{2}, and the leg opposite from the 60 degree angle is \frac{a\sqrt3}{2}

In this case, a=14, n=\frac{a}{2}, and m=\frac{a\sqrt3}{2}

Now substitute the value of a into the formulas to find n and m to find the lengths of those sides

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And m=\frac{14\sqrt3}{2}, which simplified, is equal to 7\sqrt3

Hope this helps!

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3 years ago
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