Lesson 9.1 – Trig-a-no-what???
Back in geometry class, you learned about triangles and the relationships between their
angles and sides. Today we’ll take a deeper look how angles impact the side lengths. To start,
on each of the triangles in question #1 color the shortest side red, the middle side blue and
the longest side green.
1. For each triangle below, find all missing sides and angles. (Round to the nearest
hundredth.)
2. What do the triangles have in common? What do they have that’s different?
3. Write the ratio for each pair of side lengths below. (Round to the nearest hundredth.)
△ 𝐴𝐵𝐶
△ 𝐷𝐸𝐹
△ 𝐺𝐻𝐼
red
green
blue
green
red
blue
What do you notice about the ratios?
!
4. Use the diagram to find all the missing sides and angles if tan 18° = ".
5. For some right triangle, sin 𝐴 = 0.6. What could the side lengths be? Explain.
Lesson 9.1 – Right Triangle Trigonometry
QuickNotes:
Check Your Understanding
1. Draw a right triangle with cos 60° = 0.5. Label all the sides and angles.
#
2. In a right triangle, sin 22.6° = !" . Find cos 22.6°. Draw a picture to help solve.
3. In a right triangle, tan 𝐴 = 1.5. Which side is longer, the opposite or adjacent side?
Explain.
"
4. Is it possible to have a right triangle where sin 𝜃 = $? Explain.