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A tree casts a shadow 130 feet. If the angle of the elevation is 47, which is the closest to the distance from the top of the tree to the tip of the shadow

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kudzordzifrancis

ANSWER

191 is closest to nearest whole number.

EXPLANATION

Let the distance from the top of the tree to the tip of the shadow be l feet as shown in the diagram.

This is the same as the hypotenuse of the right triangle.

The given side length, 130 ft is adjacent to the angle of elevation which is 47°

We use the cosine ratio to obtain,

[tex] \cos(47 \degree)= \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos(47 \degree)= \frac{130ft}{l} [/tex]

[tex]l= \frac{130ft}{\cos(47 \degree)} [/tex]

[tex]l =190.6162941[/tex]

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abidemiokin

The closest distance from the top of the tree to the tip of the shadow is 190.6

Application of SOH CAH TOA identity

Given the following parameters

Length of the shadow = 130feet

Angle of elevation = 47 degrees

The given side length, 130 ft is adjacent to the angle of elevation which is 47°, hence;

cos 47 = adj/hyp
cos 47 = 130/l

l = 130/cos47
l = 130/0.6819

l = 190.6

Hence the closest distance from the top of the tree to the tip of the shadow is 190.6

Learn more on angle of elevation here: https://brainly.com/question/88158

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