A tree 10 meters high casts a 17.3 meter shadow.

Mathematics

1 answer:

sashaice [31]3 years ago

5 0

Answer:

the angle of elevation of the sun is $\approx 30^o$

Step-by-step explanation:

Let's make a diagram of the tree, ground and inclination of the rays of the sun, so we understand what right angle triangle we have. Please see the attached image.

Notice that our unknown is the angle $\theta$ , and that we know the size of the side opposite to it, and of the side adjacent to it. Therefore the most convenient trigonometric formula to use is the tangent of the angle because:

$tan(\theta)=\frac{opposite}{adjacent} \\tan(\theta)=\frac{10}{17.3}\\\theta=arctan(\frac{10}{17.3})\\\theta\approx 30^o$

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