Math presentation Math presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentationMath presentation

1. (GEOMETRY)
Applying Trigonometry
OBJECTIVES:
• Solve real-world problems involving angle of elevation and
angle of depression.
• Derive and use a formula for the area of a triangle by using
trigonometry.
SUGGESTED PRACTICE:
• To Be Announced/Posted.
BOOK REFERENCE
HMH – into Geometry:
• Unit 7 - Module 13 – Lesson 13.4

2. PREVIOUSLY
• You solved problems using trigonometric ratios and
their inverses for acute angles.
NOW
• You are going to apply trigonometry to real life
situation and to triangle area.
NEXT
• You will solve problems using the law of sines.

3. DEVELOP

4. VOCABULARY
• Indirect measurement
• Angle of elevation
• Angle of depression

5. PREREQUISITE SKILLS
• Using similar triangles to measure indirectly.

6. WARM-UP (Pg. 1)

7. WARM-UP (Pg. 2)

8. LEARN: Angles of Elevation and Depression

9. Example 1 Angle of Elevation
(To Be Solved Interactively)

10. Check

11. Example 2 Angle of depression
(To Be Solved Interactively)

12. Check

13. Example 3 Use Two Angles of Elevation and Depression
(To Be Solved Interactively)

14. Check
From a 120 feet tall lighthouse, and looking in the same
direction, Hamad sees two fishing boats. He sees the first one at
a 25° angle of depression, and sees the other at a 70° angle of
depression. Calculate the distance between the two boats to the
nearest foot .
120 ft.

15. LEARN: The Area of a Triangle Using Sine
𝒉
𝐵 𝐶
𝐴
Assume that in triangle 𝐴𝐵𝐶 the two marked sides and their included
angle are given.
𝑐
𝑏
✓
✓
✓
• Find ℎ in terms of the given.
(discuss with teammates and wait)
• Substitute the expression for ℎ
into the formula for the area.
(discuss with teammates and wait)
• Rewrite the formula given another two sides and their included angle.
(discuss with teammate and wait)
Area =
𝑎𝑏 sin 𝐶
2 𝑎

16. LEARN: Trigonometry and Areas of triangles

17. Example 4 Find the Area of a Triangle When given the Included
Angle
(To Be Solved Interactively)

18. Check

19. Example 5 Find the Area of Any Triangle
(To Be Solved Interactively)

20. Check

21. The area of triangle 𝐴𝐵𝐶 is 50 cm2.
9 cm
15 cm
𝐴
𝐵
𝐶
In triangle 𝐴𝐵𝐶, angle 𝐴𝐵𝐶 is acute, 𝐴𝐵 = 9 cm and 𝐵𝐶 = 15 cm.
a. Calculate angle 𝐴𝐵𝐶.
b. Calculate the length of side 𝐴𝐶.
NOT TO
SCALE
Example 6 Find the Area of Any Triangle
(To Be Solved Interactively)

22. EXIT TICKET