Problemas
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?
Roztwór
María José
professionell · Tutor durante 6 años
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(242 Votos)
Respuesta
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.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.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:tan(42 degrees) = height of Tree A / 1.5 metersSolving for the height of Tree A, we get:height of Tree A = tan(42 degrees) * 1.5 meters ≈ 1.107 metersFor Tree B, the angle of elevation is 36 degrees, and the adjacent side is 1.5 meters. So, we can set up the equation:tan(36 degrees) = height of Tree B / 1.5 metersSolving for the height of Tree B, we get:height of Tree B = tan(36 degrees) * 1.5 meters ≈ 1.029 metersTo find the difference in height between the two trees, we subtract the height of Tree B from the height of Tree A:Difference in height = height of Tree A - height of Tree B ≈ 1.107 meters - 1.029 meters ≈ 0.078 metersTherefore, one tree is approximately 0.078 meters taller than the other.