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Find the value of each variable for the right triangles. Make sure all answers are in reduced radical from. Shoe your work.

Find the value of each variable for the right triangles Make sure all answers are in reduced radical from Shoe your work class=

Respuesta :

Denote each of the triangles ABC, where B is the right angle.

a.

[tex] t^{2}+ 12^{2}= 13^{2} [/tex]

instead of taking the square of 12 and 13, , take 12 squared to the right side and apply the difference of squares formula: [tex] a^{2}- b^{2}=(a-b)(a+b)[/tex]

[tex]t^{2}= 13^{2}- 12^{2}=(13-12)(13+12)=1*25[/tex]

so t is square root of 25, which is 5

b. 

[tex] a^{2}+9 ^{2} = 12^{2} [/tex]

[tex]a^{2}= 12^{2} -9 ^{2}=(12-9)(12+9)=3*21=3*3*7 [/tex]

[tex]a= \sqrt{3*3*7}=3 \sqrt{7} [/tex]


b.

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

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

here we can factorize 9, to work with small numbers:

[tex]9(4+9)= x^{2}[/tex]

[tex]9*13= x^{2} [/tex]

[tex] x^{2} =3*3*13[/tex]

[tex]x= \sqrt{3*3*13}=3 \sqrt{13} [/tex]
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