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In the diagram, the length of YZ is twice the length of AZ.

YA is an altitude of ΔXYZ. What is the length of YA?

A) 5 [tex] \sqrt{3} [/tex] units
B) 10 [tex] \sqrt{3} } [/tex] units
C) 15 units
D) 20 units

In the diagram the length of YZ is twice the length of AZ YA is an altitude of ΔXYZ What is the length of YA A 5 tex sqrt3 tex units B 10 tex sqrt3 tex units C class=

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MathG33k
This is a 30-60-90 triangle. There is a simple rule to finding the length of each side. The side opposite to the 30 degree angle is regarded as the value "s". In this case, length AZ is considered to be length "s". The side opposite to the right angle is considered to be "2s" and the remaining side length is [tex]s \sqrt{3} [/tex] Using this, we can find what length "s" is by dividing 10 by 2, which is 5. We multiply this value by the square root of 3 according to the rule, and the final answer is A) [tex]5 \sqrt{3} [/tex]
aksnkj

The given triagles are right angles triangle. The length of side AY is [tex]5\sqrt3[/tex] units.

Given information:

The length of side YZ is twice the length of side AZ.

The length of side YZ is 10 units.

Triangle XYZ and AXY are right angled triangles.

Now, the length of side AZ will be,

[tex]AZ=\dfrac{YZ}{2}\\AZ=\dfrac{10}{2}=5[/tex]

Now, in triangle AYZ, AZ=5, YZ=10. So, the value of angle Z will be,

[tex]{cos} Z=\dfrac{AZ}{YZ}\\{cos} Z=\dfrac{1}{2}\\Z=60^{\circ}[/tex]

So, the length of AY will be,

[tex]sinZ=\dfrac{AY}{YZ}\\sin60^{\circ}=\dfrac{AY}{10}\\AY=5\sqrt3[/tex]

Therefore, the length of side AY is [tex]5\sqrt3[/tex] units.

For more details, refer to the link:

https://brainly.com/question/3772264

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