1. April 21, 2017 The Law of Sines Topic List for Test
Geometry
April 21, 2017
The Law of Sines
Topic List for Test

2. What is the length of the hypotenuse? How tall is the triangle?
Do Now: Answer ALL FIVE
What is the length of the hypotenuse?
How tall is the triangle?
How wide is it?
tan 𝐴 =
𝑚∠𝐴= A

3. I can apply the Pythagorean Theorem and the trigonometric ratios
Chapter Objective
I can apply the Pythagorean Theorem and the trigonometric ratios

4. Today’s Objectives
Apply the Law of Sines
Review topics for the test

5. Here’s another triangle…
Divide the sine by the opposite side:
sin 40.4° /4.4 =
sin 35° /3.9=
sin 104.6° /6.5=

6. Here’s another triangle…
Divide the sine by the opposite side:
sin 54.2° /5.0 =
sin 73.3° /5.9=
sin 52.5° /4.9=

7. sin 𝐴 𝑎 = sin 𝐵 𝑏 = sin 𝐶 𝑐 The Law of Sines
For ANY triangle, the ratio of the sine of each angle and its opposite side is constant:
sin 𝐴 𝑎 = sin 𝐵 𝑏 = sin 𝐶 𝑐

8. Solve for BC sin 93° 15 = sin 48° 𝐵𝐶 𝐵𝐶= 15 sin 48° sin 93° 𝐵𝐶≈11.16
Example
Solve for BC
sin 93° 15 = sin 48° 𝐵𝐶
𝐵𝐶= 15 sin 48° sin 93°
𝐵𝐶≈11.16

9. Solve for 𝑚∠𝑆 sin 𝑆 11 = sin 120° 18 𝑚∠𝑆= sin −1 11 sin 120° 18
Example
Solve for 𝑚∠𝑆
sin 𝑆 11 = sin 120° 18
𝑚∠𝑆= sin − sin 120° 18
𝑚∠𝑆≈31.95°

10. Solve for x

11. Solve for x

12. Solve for x

13. Practice

14. The Pythagorean Theorem
A triangle is a right triangle IF AND ONLY IF it satisfies the equation:
𝑎2 + 𝑏2 = 𝑐2

15. Pythagorean Triples
A Pythagorean triple is a set of positive integers that form a right triangle.
Some common Pythagorean triples include:
3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25

16. Review Special Triangles

17. SINE The ratio of the OPPOSITE LEG to the HYPOTENUSE
INCREASES as the angle measure INCREASES
sin 𝛼 = 𝑂 𝐻

18. COSINE The ratio of the ADJACENT LEG to the HYPOTENUSE
DECREASES as the angle measure INCREASES
cos 𝛼 = 𝐴 𝐻

19. TANGENT The ratio of the OPPOSITE LEG to the ADJACENT LEG
INCREASES as the angle measure INCREASES
tan 𝛼 = 𝑂 𝐴

20. Sin, Cos, Tan
ANGLE MEASURE
RATIO OF LENGTHS
Sin-1, Cos-1, Tan-1

21. Think about… This is called the angle of ELEVATION.
This is called the angle of DEPRESSION.