Use trigonometry to help you solve the following. A pérson is standing halfway between two trees that are 3m apart. The angles of elevation to the tops of the trees are 42^circ and 36^circ How much taller is one tree over the other?

To solve this problem, we can use trigonometry. Let's label the trees as Tree A and Tree B, with Tree A being the taller tree. The person is standing halfway between the two trees, so the distance from the person to each tree is 1.5 meters.<br /><br />We can use the tangent function to find the height of each tree. The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side.<br /><br />For Tree A, the angle of elevation is 42 degrees, and the adjacent side is 1.5 meters. So, we can set up the equation:<br /><br />tan(42 degrees) = height of Tree A / 1.5 meters<br /><br />Solving for the height of Tree A, we get:<br /><br />height of Tree A = tan(42 degrees) * 1.5 meters ≈ 1.107 meters<br /><br />For Tree B, the angle of elevation is 36 degrees, and the adjacent side is 1.5 meters. So, we can set up the equation:<br /><br />tan(36 degrees) = height of Tree B / 1.5 meters<br /><br />Solving for the height of Tree B, we get:<br /><br />height of Tree B = tan(36 degrees) * 1.5 meters ≈ 1.029 meters<br /><br />To find the difference in height between the two trees, we subtract the height of Tree B from the height of Tree A:<br /><br />Difference in height = height of Tree A - height of Tree B ≈ 1.107 meters - 1.029 meters ≈ 0.078 meters<br /><br />Therefore, one tree is approximately 0.078 meters taller than the other.