Question

1. the angle of elevation of the sun is 68° when a tree casts a shadow 14.3 m long. how tall is the tree, to the nearest tenth of a meter?

○ 35.4 m
○ 36.7 m
○ 36.9 m
○ 34.1 m

Explanation:

Step1: Identify the trigonometric relationship

We can model this situation as a right triangle, where the height of the tree is the opposite side (\(h\)) to the angle of elevation (\(\theta = 68^\circ\)), and the length of the shadow is the adjacent side (\(x = 14.3\) m). The tangent function relates the opposite and adjacent sides: \(\tan(\theta)=\frac{h}{x}\).

Step2: Solve for the height of the tree

Rearrange the formula to solve for \(h\): \(h = x\times\tan(\theta)\). Substitute \(x = 14.3\) m and \(\theta = 68^\circ\) into the formula. First, calculate \(\tan(68^\circ)\approx2.475\). Then, \(h = 14.3\times2.475\approx35.4\) m.

Answer:

35.4 m (corresponding to the option "35.4 m")