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What is the measure of z?

What Is The Measure Of Z class=

Sagot :

Answer:

[tex]3 \sqrt{13} [/tex]

Step-by-step explanation:

Use altitude mean Theorem.

"If a triangle altitude splits it up into two right triangles and we are given the side left and right of the altitude then we can use the formula,

[tex] {a}^{2} = lr[/tex]

where a is the altitude, l is the left side of the altitude and r is the right side of the altitude.

We are trying to find the value of a, and we know the lr is

4*9=36

[tex] {a}^{2} = 36[/tex]

[tex]a = 6[/tex]

So we know the altitude is 6.

Know since the right triangle form a right triangle, apply Pythagoren Theorem

[tex] {6}^{2} + {9}^{2} = {r}^{2} [/tex]

[tex]36 + 81 = {r}^{2} [/tex]

[tex]117 = {r}^{2} [/tex]

[tex] \sqrt{117} = r[/tex]

[tex] \sqrt{9} \times \sqrt{13} = r[/tex]

[tex]3 \sqrt{13} = r[/tex]