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J Pause If the sun is at an angle of 30 degrees from the horizontal and a tree casts a 15-meter shadow on the ground, which is the closest height of the tree? 30° 15 m 0 A 26.0 m OB. 8.7 m o C. 13.0 m O D. 7.5 m

J Pause If the sun is at an angle of 30 degrees from the horizontal and a tree casts a 15meter shadow on the ground which is the closest height of the tree 30 1 class=

Respuesta :

Let us draw a figure to better understand the problem

From the trigonometric ratios, we know that

[tex]\tan \theta=\frac{\text{opposite}}{\text{adjacent}}[/tex]

Let us substitute the given values and find the height (h) of the tree

[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \tan (30\degree)=\frac{h}{15} \\ h=\tan (30\degree)\times15 \\ h=0.577\times15 \\ h=8.7\: m \end{gathered}[/tex]

Therefore, the height of the tree is closest to 8.7 m

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