Question

assuming that a 335 - foot tall giant redwood grows vertically, if i walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be ( 56^{circ} ), how far from the base of the tree am i? round to nearest foot. feet question help: video message instructor

Explanation:

Step1: Set up the trigonometric ratio

We know that in a right - triangle (where the tree is the vertical side, the distance from the base of the tree is the adjacent side, and the line of sight is the hypotenuse), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 56^{\circ}\), the opposite side \(y = 335\) feet, and the adjacent side \(x\) is the distance from the base of the tree. So, \(\tan(56^{\circ})=\frac{335}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{335}{\tan(56^{\circ})}\).
We know that \(\tan(56^{\circ})\approx1.4826\). Then \(x=\frac{335}{1.4826}\).

$$x=\frac{335}{1.4826}\approx226$$

Answer:

226