Join Now
View Cart
NCTM Store

Spring Up, Fall Back

  • Classroom Resources / Problems of the Week

    Spring Up, Fall Back


    PoW ID: 4707

    Problem Print

    The solar panels mounted on the side of our porch can be set to two different angles. The top small picture shows the angle for winter, when the sun is lower in the sky. The bottom one shows the angle for summer, when the sun is higher.


    Notice that there are two holes in the rails where they attach to the bottom of the panels, one hole for each angle. The rails and panels are mounted to the porch in such a way that they can swing up and down. The edge of the panel as shown in the small pictures is 18.5 inches long.

    We'd like to make a new rail so that we can set the panels to 26, 44, or 61 degrees. That measurement refers to the angle the panel makes with a horizontal line from the porch, not to the angle the panel makes with the rail.

    1. How far from the mounting point of the panel should we mount the new rail on the porch so that the rail and the porch form a 90-degree angle when the panel forms a 44-degree angle with the horizontal?

    2. How far along the rail should we drill holes so that the panels can be positioned at 26, 44, or 61 degrees?  

    Answer Check

    Show Answer

    The mounting point of the rail should be 12.85 inches from the mounting point of the panel.

    The hole in the rail for the 44-degree triangle should be 13.31 inches from the porch end. The hole in the rail for the 26-degree situation should be 17.29 inches from the porch end. The hole in the rail for the 61-degree situation should be 9.57 inches from the porch end.


    If your answer does not match our answer,

    • did you start with a right triangle with a hypotenuse of 18.5 inches and one angle of 44 degrees?
    • did you try using some right triangle trigonometry?
    • did you notice that for the 26 and 61 degree angles, you don't have a right triangle? You'll need to draw in a horizontal line yourself.

    If your answer does match ours,

    • did you explain your work as well as you can?
    • did you make any mistakes? How did you find them?
    • what hints would you give another student?