options: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Explain and use the relationship between the sine and cosine of complementary angles.
problem_activity: Problem 1
Brandon and Madison use different triangles to determine the slope of the line shown below.
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Brandon started at (0,-1) and drew a right triangle going up 2 units and right 3 units.
Madison started at (-3,-3) and drew a right triangle going up 6 units and right 9 units.
Draw and label both triangles on the graph.
How can Brandon and Madison use their triangles to find the slope?
What trigonometric ratio do Brandon and Madison use to find the slope?
Problem 2
Below is a line segment on a coordinate grid.
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Draw the right triangle that you can use to find the length of this line segment.
Find the length of the line segment.
Find the measure of all of the angles of the triangle formed.
Problem 3
Standing on the gallery of a lighthouse (the deck at the top of a lighthouse), a person spots a ship at an angle of depression of 20°. The lighthouse is 28 meters tall and sits on a cliff 45 meters tall as measured from sea level.  What is the horizontal distance between the lighthouse and the ship?


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