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const2013 [10]
3 years ago
11

Find the value of each variable ​

Mathematics
2 answers:
aalyn [17]3 years ago
7 0

Answer:

x = 12\sqrt{2}

y = 12

z = 12\sqrt{3}

Step-by-step explanation:

The triangle with z as one of it's sides is a 30, 60, 90 triangle where the longest side of the triangle is 2x, the shortest side as x, and the middle side as x*sqrt of 3.

The shared line between the two triangle is 12 and z is 12*sqrt of 3

The left triangle is a 45, 45, 90 triangle where the 2 sides that look the same are the same and the hypotenuse is x sqrt of 2 so y is 12 and x is 12 sqrt of 2

PSYCHO15rus [73]3 years ago
3 0

Answer:

x = 12\sqrt{2} units

y = 12 units

z = 12\sqrt{3} units

Step-by-step explanation:

Notice that the biggest triangle is broken up into a 45-45-90 isosceles triangle with hypotenuse x and leg y, as well as a 30-60-90 triangle with hypotenuse 24 and long leg z.

Let's focus on finding z first. Remember that in a 30-60-90 triangle, the ratio of the short leg to the long leg to the hypotenuse is: 1:\sqrt{3} :2. Here, the hypotenuse is 24 and z is the longest leg, so we have the proportion:

\frac{\sqrt{3} }{2} =\frac{z}{24}

Cross-multiply:

24\sqrt{3} =2z

z = 12\sqrt{3} units

Now, let's find the smallest leg of the 30-60-90 triangle; it is simply 24/2 = 12 units. Let's move onto x and y.

Remember that in a 45-45-90 triangle, the ratio of one leg to the second leg to the hypotenuse is: 1:1:\sqrt{2}. So, since y is a leg of this triangle and the smallest leg of the 30-60-90 triangle coincides with the second leg of the 45-45-90 triangle, y = 12 units.

Finally, x is found by multiplying 12 by \sqrt{2}: 12 * \sqrt{2} = 12\sqrt{2} units

Hope this helps!

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