Lesson 1 of 5
Label the angle and sides, choose a ratio, and check the result.
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Big ideas · 1 of 8
Big ideas
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In a right triangle, the hypotenuse is opposite the right angle. Opposite and adjacent legs are named relative to the chosen acute angle; label that angle first.
The trig ratios are , , and , where , , and are the opposite, adjacent, and hypotenuse lengths. SOHCAHTOA helps match the known and unknown sides.
A -- triangle has side ratio . A -- triangle has side ratio , with the shortest side opposite .
An angle of elevation is measured upward from horizontal. State the right-angle assumption, add observer height when needed, use degree mode for degree inputs, and round only the final result with units.
Step-through
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Find the height of a vertical post when its shadow is 7 m and the sun elevation is 40 degrees.
Whole picture, 4 steps
4 steps. Tap a number or Show me how it works.
Worked example
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Worked example
Do this: Follow each step on paper before reading the result.
Mix-up alert
Do this: Explain the wrong idea and the repair.
Wrong idea: the adjacent side is always the bottom side in a drawing. Repair: adjacent depends on the marked angle and excludes the hypotenuse. Rotate the drawing or change the chosen acute angle and relabel the legs.
Tip
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Name the hypotenuse and explain why opposite and adjacent depend on which acute angle you name.
Worked example
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A right triangle has legs 7 and 24 and hypotenuse 25.
Watch
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Flashcards
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Card 1 of 8
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Find the corner first.
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Which side is the hypotenuse?
The side opposite the right angle; it is the longest side.
State SOH.
, where is the opposite length and is the hypotenuse length.
State CAH.
, where is the adjacent length and is the hypotenuse length.
State TOA.
, where and are the opposite and adjacent lengths.
What is ?
.
What is ?
.
What is ?
.
What does an elevation angle start from?
A horizontal line at the observer.
True or false
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Self-test
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6 questions. One at a time.
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Self-test
Do this: Work on paper, choose an answer, then read the feedback.
6 questions. One at a time.
Practice, not a grade. No timer. Your best score stays in this browser.
Write it
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Write it
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Match
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Connect the ideas
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