Cogito
Integrated Math 2 · Chapter 5 · Lesson 2
Solving Right Triangles
Finding a missing side or angle.
12 problems · about 21 minutes · G-SRT.C.8
What this lesson teaches
The student uses trigonometric ratios and inverses to find missing sides and angles.
- Choose the ratio containing what you know and what you want.
- Use an inverse function when the unknown is an angle.
- Check that the hypotenuse is longest and the angles are acute.
Warm Up
Straightforward practice. Get the method working first.
5 problemsLegs 6 and 8. What is the hypotenuse?
Answer 10
Why 10.
Two sides are known and you want the angle. What do you use?
Answer An inverse trigonometric function.
Why An inverse gives the angle back.
Legs 7 and 24. Hypotenuse?
Answer 25
Why √625.
Legs 8 and 15. Hypotenuse?
Answer 17
Why √289.
tan θ = 1. What is θ, in degrees?
Answer 45
Why Equal legs.
Build It Up
The same ideas with more to keep track of.
3 problemssin θ = 0.5. What is θ, in degrees?
Answer 30
Why A special triangle.
Which ratio holds opposite and adjacent? 1 sine, 2 cosine, 3 tangent.
Answer 3
Why No hypotenuse in it.
Hypotenuse 20, opposite 10. Sine as a decimal?
Answer 0.5
Why 10 ÷ 20.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsPut the solving process in order.
Answer 1. Mark the angle you are working from. 2. Label the sides opposite, adjacent and hypotenuse. 3. Choose the ratio holding what you know and want. 4. Substitute and solve, then check the answer is sensible.
Why Labelling depends on which angle you chose.
Legs 20 and 21. Hypotenuse?
Answer 29
Why √841.
The Ladder: A right triangle has legs 9 and 12. What is the hypotenuse?
Answer 15
Why 15.
The Equal Legs: A right triangle has equal legs. What is each acute angle, in degrees?
Answer 45 degrees
Why 45°.