Dado o triângulo retângulo ABC, reto em A, representado na figura abaixo, calcule os valores desconhecidos ( x, m, n e h ).
Anexos:
Soluções para a tarefa
Respondido por
373
Bom dia Ana!
Solução!
Para determinar os valores das variáveis,basta lembrara das relações metrica no triângulo retângulo!
![a=5\\\\\
x=b=?\\\\\\
c=3\\\\\\
Teorema~~de~~Pitagoras!\\\\\\\
a^{2}=x^{2}+c^{2}\\\\\\
5^{2}= x^{2} +3^{2}\\\\\\\
25= x^{2} +9\\\\\\
25-9= x^{2} \\\\\
16= x^{2} \\\\\\
x= \sqrt{16}\\\\\\
\boxed{x=4}](https://tex.z-dn.net/?f=a%3D5%5C%5C%5C%5C%5C%0Ax%3Db%3D%3F%5C%5C%5C%5C%5C%5C%0Ac%3D3%5C%5C%5C%5C%5C%5C%0ATeorema%7E%7Ede%7E%7EPitagoras%21%5C%5C%5C%5C%5C%5C%5C%0Aa%5E%7B2%7D%3Dx%5E%7B2%7D%2Bc%5E%7B2%7D%5C%5C%5C%5C%5C%5C%0A5%5E%7B2%7D%3D+x%5E%7B2%7D+%2B3%5E%7B2%7D%5C%5C%5C%5C%5C%5C%5C%0A25%3D+x%5E%7B2%7D+%2B9%5C%5C%5C%5C%5C%5C%0A25-9%3D+x%5E%7B2%7D+%5C%5C%5C%5C%5C%0A16%3D+x%5E%7B2%7D+%5C%5C%5C%5C%5C%5C%0Ax%3D+%5Csqrt%7B16%7D%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bx%3D4%7D+++%0A+++%0A%0A "a=5\\\\\
x=b=?\\\\\\
c=3\\\\\\
Teorema~~de~~Pitagoras!\\\\\\\
a^{2}=x^{2}+c^{2}\\\\\\
5^{2}= x^{2} +3^{2}\\\\\\\
25= x^{2} +9\\\\\\
25-9= x^{2} \\\\\
16= x^{2} \\\\\\
x= \sqrt{16}\\\\\\
\boxed{x=4}")
![b^{2}=a.n\\\\\\
4^{2} =5.n\\\\\\
16 =5.n\\\\\\
\boxed{n= \frac{16}{5}}\\\\\\\\\
Altura!\\\\\\
b.c=a.h\\\\\
4.3=5.h\\\\\
12=5h\\\\\\
\boxed{h= \dfrac{12}{5}}\\\\\\\](https://tex.z-dn.net/?f=b%5E%7B2%7D%3Da.n%5C%5C%5C%5C%5C%5C%0A4%5E%7B2%7D+%3D5.n%5C%5C%5C%5C%5C%5C%0A16+%3D5.n%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bn%3D+%5Cfrac%7B16%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0AAltura%21%5C%5C%5C%5C%5C%5C%0Ab.c%3Da.h%5C%5C%5C%5C%5C%0A4.3%3D5.h%5C%5C%5C%5C%5C%0A12%3D5h%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bh%3D+%5Cdfrac%7B12%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%5C%0A%0A%0A "b^{2}=a.n\\\\\\
4^{2} =5.n\\\\\\
16 =5.n\\\\\\
\boxed{n= \frac{16}{5}}\\\\\\\\\
Altura!\\\\\\
b.c=a.h\\\\\
4.3=5.h\\\\\
12=5h\\\\\\
\boxed{h= \dfrac{12}{5}}\\\\\\\")
![m+n=a\\\\\\
m+ \frac{16}{5}=5\\\\
5m+16=25\\\\\\
5m=25-16\\\\\\
5m=9\\\\\\\
\boxed{m= \dfrac{9}{5}} \\](https://tex.z-dn.net/?f=m%2Bn%3Da%5C%5C%5C%5C%5C%5C%0Am%2B+%5Cfrac%7B16%7D%7B5%7D%3D5%5C%5C%5C%5C%0A5m%2B16%3D25%5C%5C%5C%5C%5C%5C%0A5m%3D25-16%5C%5C%5C%5C%5C%5C%0A5m%3D9%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bm%3D+%5Cdfrac%7B9%7D%7B5%7D%7D+++%5C%5C "m+n=a\\\\\\
m+ \frac{16}{5}=5\\\\
5m+16=25\\\\\\
5m=25-16\\\\\\
5m=9\\\\\\\
\boxed{m= \dfrac{9}{5}} \\")
Bom dia!
Bons estudos!
Solução!
Para determinar os valores das variáveis,basta lembrara das relações metrica no triângulo retângulo!
Bom dia!
Bons estudos!
Respondido por
7
Resposta:
x= 4 h= 2,4 m= 1,8 n= 3,2
Explicação passo-a-passo:
c²= a.m
3²= 5.m
9= 5m
5m= 9
m= 9/5
m= 1,8
h²= m.n
h²= 1,8 . 3,2
h²= 5,76 2,4 . 2,4= 5,76
h= √5,76
h= 2,4
5-1,8= 3,2
espero ter ajudado
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