Question

question 13 (technology required) the sun is 62 degrees above the horizon. a tree casts a shadow that is 12 feet long. how tall is the tree? round to the nearest tenth. answer (in feet):

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the shadow length is the adjacent side (\(a = 12\) feet) to the angle of elevation (\(\theta=62^\circ\)), and the height of the tree (\(h\)) is the opposite side. We use the tangent function: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}=\frac{h}{12}\).

Step2: Solve for \(h\)

Rearrange the formula: \(h = 12\times\tan(62^\circ)\). Calculate \(\tan(62^\circ)\approx1.8807\). Then \(h = 12\times1.8807\approx22.57\) (rounded to two decimal places) or as per the problem's requirement (nearest tenth: \(22.6\)).

Answer:

\(22.6\) (or \(22.57\) depending on precision, but nearest tenth is \(22.6\))