The sun is 30° above the horizon. It makes a 52-m-long shadow of a tall tree. How high is the tree?
ANSWER: STEP 1:- The sun is 30° above the horizon, that means it makes an angle of 30° with the horizontal plane. To illustrate this, we require a schematic diagram which is shown below. In the above figure, AB line represents the tree and BC line represents the distance from the tree. As the sun light incidents on top of the tree, the shadow it will create will be equal to the length of BC line which is 52 m. The above diagram looks like a right angled triangle ABC, whose base we know already. Here, AB is the perpendicular or the height of right angle triangle, BC is the base and AC is the hypotenuse. STEP 2:- Having the angle and base we can calculate the height very easily. 0 = 30 0 tan = tan 30 0 perpendicular / base = tan 30 height / BC = 0.577 height / 52 = 0.577 height = 0.577×52 height = 30.022 m The reason to choose the “tan” ratio of 30 is because “tan” is the only ratio which has the information about both height and base simultaneously. “Cot” function can also be used, as it is the reciprocal of “tan” function. So the student is challenged to do the problem with the help of “cot” function CONCLUSION: So, we found that the height of the tree would be 30 meter approximately.