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Jane, who is
1.7m tall, is standing
8m from a
5m tall tree. She looks up to the top of the tree and measures the angle of elevation. What measure did she find?

$1$ . Jane, who is $1.7 \mathrm{~m}$ tall, is standing $8 \mathrm{~m}$ from a $5 \mathrm{~m}$ tall tree. She looks up to the top of the tree and measures the angle of elevation. What measure did she find?

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Pythagorean theorem: word problems

Full solution

Q.

1

. Jane, who is

1.7 \mathrm{~m}

tall, is standing

8 \mathrm{~m}

from a

5 \mathrm{~m}

tall tree. She looks up to the top of the tree and measures the angle of elevation. What measure did she find?

Identify Triangle: Identify the triangle formed by Jane, the base of the tree, and the top of the tree. Jane's eye level is $1.7\,\text{m}$ , so the tree's height relative to her eye level is $5\,\text{m} - 1.7\,\text{m} = 3.3\,\text{m}$ . The distance from Jane to the tree is $8\,\text{m}$ .
Use Tangent Function: Use the tangent function, which relates the angle of elevation $\theta$ to the opposite side (height difference) and the adjacent side (horizontal distance). $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{3.3\,\text{m}}{8\,\text{m}}$ .
Calculate Tangent Value: Calculate the tangent value. $\tan(\theta) = \frac{3.3}{8} = 0.4125$ .
Find Angle: Find the angle $\theta$ by taking the arctan of $0.4125$ . $\theta = \arctan(0.4125)$ . Using a calculator, $\theta \approx 22.38$ degrees.

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