The angle of elevation to a nearby tree from a point on the ground is measured to be 64^(@). How tall is the tree if the point on the ground is 49 feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary.

Question

The angle of elevation to a nearby tree from a point on the ground is measured to be  64^(@). How tall is the tree if the point on the ground is 49 feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary.

Bytelearn · Accepted Answer

Understand Problem: Understand the problem and identify the right trigonometric function to use. We are given the angle of elevation to the top of the tree and the distance from the point on the ground to the bottom of the tree. To find the height of the tree, we can use the tangent function, which relates the angle of elevation to the opposite side (height of the tree) and the adjacent side (distance from the tree).Set Up Equation: Set up the equation using the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. So, we have: tan(64°) = (height of the tree) / (distance from the tree)Plug in Values: Plug in the known values into the equation. tan(64°) = (height of the tree) / 49 feetCalculate Tangent: Calculate the tangent of 64 degrees using a calculator. tan(64°) ≈ 2.050303841Solve for Height: Solve for the height of the tree. (height of the tree) = tan(64°) * 49 feet (height of the tree) ≈ 2.050303841 * 49 feetPerform Multiplication: Perform the multiplication to find the height of the tree. (height of the tree) ≈ 100.464889209 feetRound Answer: Round the answer to the nearest hundredth of a foot. (height of the tree) ≈ 100.46 feet

The angle of elevation to a nearby tree from a point on the ground is measured to be $64^{\circ}$ . How tall is the tree if the point on the ground is $49$ feet from the bottom of the tree? Round your answer to the nearest hundredth 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 64∘ 64^{\circ} 64∘. How tall is the tree if the point on the ground is 494949 feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary.

The angle of elevation to a nearby tree from a point on the ground is measured to be $64^{\circ}$ . How tall is the tree if the point on the ground is $49$ feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary.