Find the exact lengths of the altitudes of right triangles B and C.
The right triangle B's altitude length is ?
The right triangle C's altitude length is ?
The right triangle B and c altitude length are same that is 6.
Given that,
In the given picture there are 2 right triangles.
They are B and C.
2 sides of the triangle B is 3 and [tex]3\sqrt{3}[/tex].
2 sides of the triangle C is 6 and [tex]6\sqrt{2}[/tex].
The angle for both the right triangle B and C is 90°.
We have to find the length of the altitude of right triangles B and C.
By using the Pythagorean theorem we can find the length of the altitude of the right triangle B and C.
The simplest way is to use the Pythagorean theorem if you are aware of two additional right triangle sides:
[tex]a^{2} +b^{2} =c^{2}[/tex]
Where the sides of the right triangle are a, b, and c.
First, We will find for the right triangle B.
Here, a=[tex]3\sqrt{3}[/tex] and b=3
Now, substitute in the formulae
[tex](3\sqrt{3})^{2} +3^{2}=c^{2}[/tex]
[tex]27+9=c^{2}[/tex]
[tex]36=c^{2} \\[/tex]
[tex]c^{2} =36\\[/tex]
Taking square root on both sides
[tex]\sqrt{c^{2} } =\sqrt{36}[/tex]
[tex]c=6[/tex]
Therefore, the length of the altitude of right triangle B is 6.
Now, We will find for the right triangle C.
Here, b=6 and c=[tex]6\sqrt{2}[/tex]
Now, substitute in the formulae
[tex]a^{2} +6^{2}=(6\sqrt{2}) ^{2}[/tex]
[tex]a^{2} +36=72[/tex]
[tex]a^{2}=72-36 \\[/tex]
[tex]a^{2} =36\\[/tex]
Taking square root on both sides
[tex]\sqrt{a^{2} } =\sqrt{36}[/tex]
[tex]a=6[/tex]
Therefore, the length of the altitude of right triangle B is 6.
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