Question

1. set up a trig ratio and solve for the missing distance, x, to find how far a random person is from the base of a random tall thing. round your answer to the nearest foot. please show work on your study guide! random tall thing random person 20ft 35° x

Explanation:

Step1: Identify trig ratio

We have a right triangle with opposite side (height of tall thing) = 20 ft, angle = \(35^\circ\), and adjacent side \(x\) (distance from person to base). Use tangent: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\)
\(\tan(35^\circ)=\frac{20}{x}\)

Step2: Solve for \(x\)

Rearrange formula: \(x = \frac{20}{\tan(35^\circ)}\)
Calculate \(\tan(35^\circ)\approx0.7002\)
\(x=\frac{20}{0.7002}\approx28.56\), round to nearest foot: \(x\approx29\)

Answer:

\(x \approx 29\) feet