Cogito
Trigonometry · Chapter 1 · Lesson 1
Solving Right Triangles
Choose the ratio that has what you know.
8 problems · about 19 minutes · G-SRT.C.8
What this lesson teaches
The student solves right triangles and applies trigonometry to angles of elevation and depression.
- Label the sides relative to your chosen angle.
- Pick the ratio containing what you know and what you want.
- The hypotenuse is always the longest side.
Warm Up
Straightforward practice. Get the method working first.
4 problemsLegs 20 and 21. Hypotenuse?
Answer 29
Why 29.
Which ratio involves the opposite and adjacent sides?
Answer Tangent.
Why Tangent.
Legs 7 and 24. Hypotenuse?
Answer 25
Why 49 + 576 = 625.
Opposite 8, hypotenuse 10. Sine, as a decimal?
Answer 0.8
Why 8 ÷ 10.
Build It Up
The same ideas with more to keep track of.
2 problemsAdjacent 6, hypotenuse 10. Cosine, as a decimal?
Answer 0.6
Why 6 ÷ 10.
Which side is always the longest?
Answer The hypotenuse.
Why Opposite the right angle.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Ladder: A right triangle has legs 9 and 12. What is the hypotenuse?
Answer 15
Why 15.
The Ratio: Opposite 5, adjacent 12. What is the tangent, as a decimal to two places?
Answer 0.42
Why About 0.42.