How+tall+is+your+tree?



The Objective: You will use a clinometer to make indirect measurments of tall objects. (Trees) You will use mathmatics by multiplying the Tangent of an angle to the adjacent side of a right triangle to determine the length of its opposite side. Background Information: Make indirect measurement with clinometers It is not feasible to measure the height of a tall object by running a tape measure along its length and so we must measure it indirectly by measuring other quantities directly and using the proper mathematics to calculate the height. We are going to make clinometers and use them to measure angles of elevation from our line of sight to the top of a tall object. Suppose we wanted to measure how tall a tree is, consider the following diagram. [|How tall is your tree pdf.pdf] Materials Needed:  measuring tape stiff cardboard length of string ruler, steel washer tape Download the student handouts One Clinometer per students: Clinometers will be constructed in class prior to doing the activity. Tangent chart Calculator Pre-measured length of cord for determining base of right triangle. paper and pencils Data to Collect:
 * ~  ||~ Tree one ||   ||~ Tree two ||   ||~ Tree Three ||   ||~ Tree Height ||
 * ~ Base Distance || 35 ||  || 35 ||   || 35 ||   ||   ||
 * ~ Angle ð (A) ||  ||   ||   ||   ||   ||   ||   ||
 * ~ Tangent of Angle ð ||  ||   ||   ||   ||   ||   ||   ||
 * ~ Observer Hight ||  ||   ||   ||   ||   ||   ||   ||

Standards: Grade 8 In Grade 8, all students should: M1e: apply order of operations to simplify expressions and perform appropriate operation(s) involving numbers written in exponential notation or radical form M1f: make reasonable estimates and then solve problems that include rational numbers, ratios, and proportions. M2f: solve linear equations and inequalities M2h: model and solve problems using various representations, i.e., graphs, tables, and equations M2j: analyze changes in linear relationships using graphs M2k: Describe and compare how changes in an equation affect the related graph. M3a: understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects M3e: plot ordered pairs of rational numbers on the coordinate plane in all four quadrants M3f: use geometric models to represent and explain numerical and algebraic relationships. Grade 8 M6a: build new mathematical knowledge through problem solving M6a: solve problems that arise in mathematics and in other contexts M6a: monitor and reflect on the process of mathematical problem solving. M8a: organize and consolidate their mathematical thinking through communication M8a: communicate their mathematical thinking coherently and clearly to peers, teachers, and others