The angle of elevation to a nearby tree from a point on the ground is measured to be 32^(@). How tall is the tree if the point on the ground is 71 feet from the bottom of the tree? Round your answer to the nearest tenth of a foot if necessary.

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The angle of elevation to a nearby tree from a point on the ground is measured to be  32^(@). How tall is the tree if the point on the ground is 71 feet from the bottom of the tree? Round your answer to the nearest tenth of a foot if necessary.

Bytelearn · Accepted Answer

Understand and Visualize: Understand the problem and visualize the scenario. We are given the angle of elevation from a point on the ground to the top of a tree, which is 32 degrees. We also know the distance from the point on the ground to the base of the tree, which is 71 feet. We need to find the height of the tree. This forms a right-angled triangle with the height of the tree being the opposite side, the distance from the tree being the adjacent side, and the angle of elevation being the angle between the adjacent side and the hypotenuse.Use Trigonometric Function: Use the trigonometric function to relate the angle of elevation to the height of the tree. Since we have the angle of elevation and the adjacent side, we can use the tangent function, which is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the tree). So, tan(32 degrees) = height of the tree / 71 feet.Calculate Height: Calculate the height of the tree. First, find the value of tan(32 degrees) using a calculator or trigonometric tables. tan(32 degrees) ≈ 0.624869 Now, solve for the height of the tree: height of the tree = tan(32 degrees) * 71 feet height of the tree ≈ 0.624869 * 71 height of the tree ≈ 44.366099 feetRound Answer: Round the answer to the nearest tenth of a foot. The calculated height of the tree is approximately 44.366099 feet. When rounded to the nearest tenth, it becomes 44.4 feet.

The angle of elevation to a nearby tree from a point on the ground is measured to be $32^\circ$ . How tall is the tree if the point on the ground is $71$ feet from the bottom of the tree? Round your answer to the nearest tenth of a foot if necessary.

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The angle of elevation to a nearby tree from a point on the ground is measured to be $32^\circ$ . How tall is the tree if the point on the ground is $71$ feet from the bottom of the tree? Round your answer to the nearest tenth of a foot if necessary.