The tree and the shadow make a right triangle with the tree height opposite the 68 degree angle:
[tex]\tan \theta = \dfrac{h}{s}[/tex]
[tex]h = s \tan \theta = 14.3 \tan 68^\circ = 35.3937...[/tex]
Choice C
The height of the tree to the nearest tenth is 35.4 m.
The angle of elevation of the sun is 68° when the tree cast a shadow 14.3m long.
The situation forms a right angle triangle. The height of the tree is opposite side of the triangle. The shadow length is the adjacent of the triangle. Therefore,
Using trigonometric, let's find the height of the tree.
tan 68 = opposite / adjacent
tan 68 = h / 14.3
cross multiply
h = 14.3 × tan 68°
h = 2.47508685342 × 14.3
h = 35.3937420039
h ≈ 35.4 m
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