Answer:
Option C. [tex]tan(A)=\frac{3}{4}[/tex]
Step-by-step explanation:
we know that
The tangent of angle A is equal to divide the opposite side to angle A (side BC) by the adjacent side to angle A ( side AB)
so
[tex]tan(A)=\frac{BC}{AB}[/tex]
substitute the values
[tex]tan(A)=\frac{x}{x+1}[/tex]
Applying the Pythagoras Theorem find the value of x
[tex](x+2)^{2}=x^{2}+(x+1)^{2}\\ \\x^{2}+4x+4=x^{2}+x^{2}+2x+1\\ \\x^{2} -2x-3=0[/tex]
using a graphing calculator-----> solve the quadratic equation
The solution is x=3 -----> see the attached figure
substitute the value of x in the tan(A)
[tex]tan(A)=\frac{3}{3+1}[/tex]
[tex]tan(A)=\frac{3}{4}[/tex]
