D. Development (Time Frame: 60 minutes) Example #1 Problem: A tower is 15.24 m high. At a certain distance away from the tower, an observer determines that the angle of elevation to the top of it is 41°. How far is the observer from the base of the tower? Pictures below from MATHEMATICS GRADE 9 Learner's Material, DepEd-BLR, First Edition, 2014, page 460.
Draw the diagram:
H
15.24
41°
O
B
Height of tower: 15.24 m
Angle of elevation: 41°
What are the given?
- Height of tower: 15.24 m
- Angle of elevation: 41°
What is to be determined?
- Distance from the observer to the base of the tower
Formula used:
tan θ = opposite / adjacent
Learning Phases and Learning Activities Introduction (Time Frame: 5 minutes):
This lesson shall focus on solving real-life problems about angles of elevation and depression using the six trigonometric ratios you have learned from the previous weeks. We will learn to see the world mathematically by reimagining objects into their triangular counterparts and then solving that triangle by finding the lengths of the sides or the measure of the angles of the triangle.
Steps in problem solving involving trigonometric ratios:
1. Draw a diagram. Transform it into a geometric triangle and label each part correctly.
2. Determine the given and the question that needs to be answered.
3. Identify the corresponding trigonometric formula to be used.
4. Show your solution.
5. Present the conclusion.