Cogito
Geometry · Chapter 5 · Lesson 2
Solving Right Triangles
Choosing the ratio that has what you know.
11 problems · about 24 minutes · G-SRT.C.8
What this lesson teaches
The student finds unknown sides and angles in a right triangle.
- Label the sides relative to the angle in use.
- Choose the ratio containing what you know and what you want.
- With two sides and no angle, Pythagoras is the shorter route.
Warm Up
Straightforward practice. Get the method working first.
4 problemsLegs 7 and 24. Hypotenuse?
Answer 25
Why 25.
Legs 3 and 4. Hypotenuse?
Answer 5
Why 9 + 16.
Legs 5 and 12. Hypotenuse?
Answer 13
Why 25 + 144.
Hypotenuse 13, one leg 5. Other leg?
Answer 12
Why 169 − 25.
Build It Up
The same ideas with more to keep track of.
3 problemsMatch each pair of known parts to the ratio you would use.
Answer Opposite and hypotenuse → Sine; Adjacent and hypotenuse → Cosine; Opposite and adjacent → Tangent
Why Only one ratio avoids the hypotenuse entirely.
Legs 9 and 12. Hypotenuse?
Answer 15
Why 81 + 144.
Can a leg be longer than the hypotenuse? 1 for yes, 0 for no.
Answer 0
Why Never.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsLegs 8 and 15. Hypotenuse?
Answer 17
Why 64 + 225.
Two sides known, third wanted, no angles. Use Pythagoras? 1 for yes, 0 for no.
Answer 1
Why No angle needed.
The Third Side: Legs 6 and 8. What is the hypotenuse?
Answer 10
Why 10.
The Longest Side: Which side is always longest in a right triangle? 1 for a leg, 2 for the hypotenuse.
Answer 2
Why The hypotenuse.