Getting Started 
Misconception/Error The student does not understand how to use trigonometric ratios to solve the problem. 
Examples of Student Work at this Level The student may add the given information to the diagram. However, the student:
 Indicates he or she does not know how to write an equation to solve the problem.
 Interprets 72° as the length of a side and uses the Pythagorean Theorem to find the unknown length.
 Writes an equation that does not involve a trigonometric ratio.

Questions Eliciting Thinking What are you given? What are you trying to find?
Where on the diagram is the 72º angle? Which distance is 50 yards? Did you label these on the diagram?
Can you really use the Pythagorean Theorem to find the unknown length? Were you given the lengths of two sides of the triangle?
Can this situation be modeled by a right triangle?
Could you use a trig ratio to help you find the missing length? 
Instructional Implications Review the definitions of the trigonometric ratios. Provide opportunities to apply the definitions to right triangles (presented in various orientations) by asking the student to identify the sine, cosine, and tangent ratios associated with each of the two acute angles. Then model finding an unknown length or angle measure in a right triangle by using an appropriate trigonometric ratio. Caution the student to carefully select an appropriate ratio and substitute measures correctly to write an equation. If needed, review solving equations of the form a= with the unknown in all positions.
Provide additional opportunities to find an unknown length or angle measure in right triangles by using the Pythagorean Theorem or an appropriate trigonometric ratio.
Consider implementing other MFAS tasks for GSRT.3.8. 
Moving Forward 
Misconception/Error The student makes an error in interpreting the given information or in using a trigonometric ratio to solve the problem. 
Examples of Student Work at this Level The student attempts to write an equation involving a trigonometric ratio but:
 Uses an incorrect trigonometric ratio.
 Uses the correct trigonometric ratio but writes the ratio incorrectly.
 Labels the wrong angle as 72º.
 Find the distance between the tree stump and stake 2.

Questions Eliciting Thinking Where on the diagram is the 72º angle? Which distance is 50 yards?In the right triangle, what is the relationship between the side of length 50 and the 72º angle? The side whose length you are trying to find and the 72º angle? Which trig ratio involves these two relationships?
What is the tangent ratio? What value should go in the numerator? What value should go in the denominator?
Does your answer make sense given the other measures in the problem? 
Instructional Implications Review the definitions of the trigonometric ratios. Then provide feedback to the student regarding any error made and allow the student to revise his or her work. Guide the student to carefully label given measures in diagrams and to consider if final answers make sense.
Provide additional opportunities to find an unknown length or angle measure in right triangles by using the Pythagorean Theorem or an appropriate trigonometric ratio.
Consider implementing other MFAS tasks for GSRT.3.8. 
Almost There 
Misconception/Error The student makes a minor computational or rounding error. 
Examples of Student Work at this Level The student labels the diagram correctly and writes a correct equation involving a trigonometric ratio. However, the student:
 Calculates in radians instead of degrees when using a calculator.
 Makes an error using the table of trigonometric values.
 Does not round according to the directions of the problem.

Questions Eliciting Thinking What mode should your calculator be in?
There is a small error in your work. Can you find and correct it?
Can you show me how you used the table to find tan 72º?
According to the problem, how should you express your final answer? 
Instructional Implications Provide feedback to the student regarding any error made and allow the student to revise his or her work. Provide additional opportunities to find unknown lengths or angle measures in right triangles.
Introduce the student to the concept of solving a triangle (i.e., finding all angle measures and side lengths). Ask the student to solve right triangles given minimal information (e.g., the measure of an acute angle and one side or the measures of two sides).
Consider implementing other MFAS tasks for GSRT.3.8. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student correctly labels the diagram, writes an equation involving a trigonometric ratio, solves the equation, and rounds the answer to the nearest whole yard:
tan 72º = or tan 18º = x 154 feet.

Questions Eliciting Thinking Can you think of another correct way to write the equation? How?
Can you write an equation to find the hypotenuse of the triangle? 
Instructional Implications Challenge the student to find another correct way to write the equation. Then ask the student to consider the relationship between the sine and cosine of complementary angles in the context of right triangles.
Ask the student to consider changing the problem so that the distance from Stake 1 to Stake 2 is 100 yards. Then ask the student to explain why the tan 72º has the same value regardless of the “size” of the triangle.
Consider implementing other MFAS tasks for GSRT.3.8. 