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Sagot :
Answer:
[tex]\displaystyle \tan A=\frac{4}{3}[/tex]
Step-by-step explanation:
Funciones Trigonométricas
La identidad principal en trigonometría es:
[tex]sen^2A+cos^2A=1[/tex]
Si sabemos que A es un ángulo agudo (que mide menos de 90°), su seno y coseno son positivos.
Dado que Sen A = 4/5, calculamos el coseno:
[tex]cos^2A=1-sen^2A[/tex]
Sustituyendo:
[tex]\displaystyle cos^2A=1-\left(\frac{4}{5}\right)^2[/tex]
[tex]\displaystyle cos^2A=1-\frac{16}{25}[/tex]
[tex]\displaystyle cos^2A=\frac{25-16}{25}[/tex]
[tex]\displaystyle cos^2A=\frac{9}{25}[/tex]
Tomando raíz cuadrada:
[tex]\displaystyle cos\ A=\sqrt{\frac{9}{25}}=\frac{3}{5}[/tex]
La tangente se define como:
[tex]\displaystyle \tan A=\frac{sen\ A}{cos\ A}[/tex]
Substituyendo:
[tex]\displaystyle \tan A=\frac{\frac{4}{5}}{\frac{3}{5}}[/tex]
[tex]\displaystyle \tan A=\frac{4}{3}[/tex]
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