A tree casts a shadow 15 m long on the level of ground, when the angle of elevation of the sun is 45c. the height of a tree is

The sum of the measures of all the angles in a triangle is always equal to #180^o#. In a right triangle, however, one of the angles is already known: the right angle, or the #90^o# angle. Let the other two angles be #x# and #y# (which will be acute). Applying these conditions, we can say that, #x+y+90^o=180^o# #x+y=180^o-90^o# #x+y=90^o# That is, the sum of the two acute angles in a right triangle is equal to #90^o#. If we know one of these angles, we can easily substitute that value and find the missing one. For example, if one of the angles in a right triangle is #25^o#, the other acute angle is given by: #25^o +y=90^o# #y=90^o-25^o# #y=65^o# Right triangles are a special case of triangles. You always know at least one angle, the right angle, and depending on what else you know, you can solve the rest of the triangle with fairly simple formulas. If you know any one side and one angle, or any two sides, you can use the pneumonic soh-cah-toa to remember which trig function to use to solve for others. # ul s i n( theta) =# #ul o#pposite #/# #ul h#ypotenuse # ul c os(theta) = ul a#djacent #/ul h#ypotenuse #ul t an(theta) = ul o#pposite #/ul a#djacent Opposite refers to the side which is not part of the angle, adjacent refers to the side that is part of the angle, and the hypotenuse is the side opposite the right angle, which is #C# in the image above. For example,lets say you know the length of #a# and the value of angle #A# in the above triangle. Using the cosine function y...