Question

The angle of elevation to a nearby tree from a point on the ground is measured to be 49degrees

. How tall is the tree if the point on the ground is 53 feet from the bottom of the tree? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

To find the height of the tree given the angle of elevation and the distance from the point on the ground, we can use trigonometry and the tangent function.By using the tangent function of the 49-degree angle of elevation, we calculate that the tree is approximately 65.68 feet.

Step-by-step explanation:

To find the height of the tree, we can use the concept of trigonometry.

The angle of elevation is the angle between the horizontal line and the line of sight from the ground to the top of the tree. In this case, the angle of elevation is 49 degrees.

We can consider a right triangle where the vertical side represents the height of the tree and the horizontal side represents the distance from the point on the ground to the bottom of the tree.

The tangent function relates the angle of elevation and the ratio of the height to the distance.

We can use the formula: tan(angle) = height/distance.

Substituting the values, we get: tan(49) = height/53.

Now, we can solve for height by multiplying both sides of the equation by 53: height = 53 * tan(49).

Calculating this expression, we find that the height of the tree is approximately 65.68 feet.