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.
 Writes an equation that does not involve a trigonometric ratio such as 564 = .
 Uses the Pythagorean Theorem to find the length of the third side of the triangle rather than the indicated angle.

Questions Eliciting Thinking What were you given? What are you trying to find?
Can this situation be modeled by a right triangle?
Could you use a trig ratio to help you find the missing angle? 
Instructional Implications If necessary, review the concepts of angles of elevation and depression. Guide the student to observe that in any given diagram, the angle of elevation and the angle of depression form an alternate interior pair and are therefore, congruent. Provide opportunities for the student to identify angles of elevation and depression in a variety of diagrams and contexts. 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:
 Labels the diagram incorrectly.
 Does not use the correct trigonometric ratio in the equation.
 Does not know how to solve for the angle measure.

Questions Eliciting Thinking Where is the base of the monument in the diagram? Where is the base of the flag pole in the diagram? Which part of the diagram represents the distance between the base of the flag pole and the top of the monument?
What is an angle of elevation? How is it different from an angle of depression? How are they the same?
In the right triangle, what is the relationship between the side of length 100 and the angle of elevation? The side of length 564 and the angle of elevation? Which trig ratio involves these two relationships?
What is the sine ratio? What value should go in the numerator? What value should go in the denominator?
How do you solve a trig equation when you do not know the measure of the angle? 
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.
If needed, review how to solve for the angle measurement when both values in the trig ratio are known, both with a calculator and with a table of trigonometric values.
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, writes a correct equation involving a trigonometric ratio but:
 Does not round according to the directions of the problem.
 Calculates in radians instead of degrees when using a calculator.
 Makes an error using the table of trigonometric values.
 Makes a computation error.
 Misuses notation, for example, writes = ().

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 trig table to find the angle measure?
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 degree:

Questions Eliciting Thinking Can you think of another correct way to write the equation? How?
How could you find the height of the Washington Monument? 
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.
Consider implementing other MFAS tasks for GSRT.3.8. 