As shown in the figure below, Mary is standing 95 feet from the base of a leaning tree. The tree is growing at an angle of 80° with respect to the ground. The angle of elevation from where Mary is standing to the top of the tree is 47°. Find the length, x, of the tree. Round your answer to the nearest tenth of a foot. | feet 47° 80° -95 ft

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As shown in the figure below, Mary is standing 95 feet from the base of a leaning tree. The tree is growing at an angle of 80° with respect to the ground. The angle of elevation from where Mary is standing to the top of the tree is 47°. Find the length, \( x \), of the tree. Round your answer to the nearest tenth of a foot.

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**Diagram Explanation:**

The diagram features a right triangle formed by the ground, the line of sight from Mary to the top of the tree, and the tree itself. 

- Mary is positioned on the left.
- The horizontal line (base) indicates her distance from the tree, which is 95 feet.
- A diagonal line represents the angle of elevation (47°) from Mary to the top of the tree.
- The vertical line represents the tree, which leans at an angle of 80° with respect to the ground.
- \( x \) is the length of the tree, denoted as the hypotenuse of the right triangle formed.

The goal is to solve for \( x \), utilizing trigonometric relationships in the context of the given angles and distance.
Transcribed Image Text:As shown in the figure below, Mary is standing 95 feet from the base of a leaning tree. The tree is growing at an angle of 80° with respect to the ground. The angle of elevation from where Mary is standing to the top of the tree is 47°. Find the length, \( x \), of the tree. Round your answer to the nearest tenth of a foot. --- **Diagram Explanation:** The diagram features a right triangle formed by the ground, the line of sight from Mary to the top of the tree, and the tree itself. - Mary is positioned on the left. - The horizontal line (base) indicates her distance from the tree, which is 95 feet. - A diagonal line represents the angle of elevation (47°) from Mary to the top of the tree. - The vertical line represents the tree, which leans at an angle of 80° with respect to the ground. - \( x \) is the length of the tree, denoted as the hypotenuse of the right triangle formed. The goal is to solve for \( x \), utilizing trigonometric relationships in the context of the given angles and distance.
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