Two maple leaf trees are 48 metres apart. From the point of the ground halfway between the trees, the angle of elevation to the tops of the trees are 35 degrees and 46 degrees. Determine the distance, to the nearest meter, between the two tops of the tree.
Express this problem as 2 right triangles. The first one has a base of 24, and by doing \(24 \over cos (35)\), you find that the Hypotenuse is 29.3 meters long. By doing \(29.3 * sin(35)\), you find that the height of the triangle is 16.8 meters long. By doing the same to the other triangle, you find that the height is 24.8 meters. Now, by using the Pythagorean's theorem, \(48^2 + 8^2 = x^2\), you find that the distance between the treetops is 49 meters.