Question

Given the triangle and equation below, what is the value of x?

Answer 1

csc∠A + tan∠C = 5x

Answer 2

answer choices:

Answer 3

first find the side AB by pythagorus
\[7^2=AB^2+6^2\]\[49=AB^2+36\]\[AB=\sqrt{13}\]
\[\csc(A)=\frac{1}{\sin(A)}\]\[=\frac{hypotenuse}{opposite}=\frac{7}{6}\]\\[\tan(C)=\frac{opposite}{adjacent}=\frac{\sqrt{13}}{6}\]
now substitiuting in the equation\[\frac{7}{6}+\frac{\sqrt{13}}{6}=5x\]\[x=\frac{7+\sqrt{13}}{30}\]

Answer 4

:)