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A tree casts a 16-foot-long shadow on level ground. A forestry student uses a clinometer to determine that the sun is at a 70° angle of elevation.


What is the height of the tree to the nearest whole foot?

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Respuesta :

Answer:

Tree is [tex]43.84[/tex] feet tall

Step-by-step explanation:

Shadow casted by tree [tex]= 15[/tex] feet

Angle of elevation of sun [tex]= 70[/tex] degrees

Tangent of angle of elevation is equal to the ration of height of tree and its shadow

tan [tex]70 = \frac{t}{16}[/tex]

Height of the tree is equal to [tex]16 *[/tex] tan [tex]70[/tex]

Height of the tree [tex]= 16 * 2.74 = 43.84[/tex] feet

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