Question

solve for x.
20°6x + 16
x = 24x = 9x = 144x = 54

Explanation:

Step1: Use trigonometric function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 20^{\circ}\), and the opposite side is \(6x + 16\). But we assume this is a \(20 - 70-90\) triangle. Wait, no, using \(\sin20^{\circ}=\frac{6x + 16}{hypotenuse}\) is wrong. Wait, no, if we consider the side \(6x+16\) as the opposite side to the \(20^{\circ}\) angle in a right - triangle. But wait, no, using \(\tan20^{\circ}=\frac{6x + 16}{\text{adjacent}}\) is not helpful. Wait, no, if we assume the side \(6x + 16\) is the opposite side to the \(20^{\circ}\) angle and we use the fact that \(\sin20^{\circ}\approx0.342\). But wait, no, if we substitute \(x = 9\) into \(6x+16\), we get \(6\times9+16=54 + 16=70\). If we assume some right - triangle properties (maybe a mis - drawn triangle where the side \(6x + 16\) is related to angle sum). Wait, no, another approach: substitute each value of \(x\) into \(6x+16\).
For \(x = 9\): \(6x+16=6\times9+16=54 + 16 = 70\). If we assume the triangle has angles \(20^{\circ},70^{\circ},90^{\circ}\) (since \(20+70+90 = 180\)) and if \(6x + 16\) corresponds to the \(70^{\circ}\) related side (by some proportion, but more simply substitution)

Answer:

\(x = 9\)