Lesson Plan
Finding missing side and finding missing angle
using trigonometric ratios
Inquiry:
How can trigonometric ratios help to
find a missing angle or a missing side of
right triangles?
Group Size & Materials:
Date: 2015-5-5
Time: 13:17-14:07
Duration: 50 minutes
Cycle Level: Secondary 3
By the end of this lesson, the students will be able to:
• Students will be able to use appropriately the correct ratio to
use in the given problem.
• Students will be able to use trigonometric ratios to solve for
an unknown length of a side of a right triangle, given an
angle and a length of a side.
• Students will be able to solve inverse trigonometric ratios.
• Students will be able to use trigonometric ratios to solve for
an unknown angle of a right triangle, given the length of
two sides.
• Students will demonstrate mastery in the practice problems.
28 Students
PowerPoint, Smart board
Subject Competency:
G2b i， ii，iii
Cross Curricular Competencies:
Competencies 1,2,3,5
Time
13:17-13:25
Lesson
Introduction: Review the trigonometric ratios. Review how to label the sides
according to a reference angle.
Sin(x)= opp/ hyp
Cos(x)= adj/hyp
Tan(x)=opp/adj
Development: Application of trigonometric ratios
13:25-13:30
Finding missing side:
Need: one side, one angle
Steps:
Step 1 Label the sides according to the given angle: Opposite, Adjacent or
Hypotenuse
Step 2 Choose which trigonometric ratio to use:
SOH CAH TOA
Step 3 Substitute in the values in the formula
Step 4 Solve equation
Example: Finding missing side
!3:25-13:30
•
•
•
•
Step 1 The two sides are involved are Opposite and Adjacent.
Step 2 SOH CAH TOA tells us to use Tangent
Step 3 Substitute in the values in the formula
tan (53) = opposite ⁄ adjacent
= a⁄7
Step 4 Solve equation
a = tan (53) x 7
= 1.327 x 7
= 9.29
The measure of side “ a “ is 9.29
13:30-13:40
Two practice questions for finding missing side and verify the answer with
them
13:40- !3:50
Finding missing angle:
Need: two sides
Steps
• 1. Step 1 Label the sides according to the angle that you are trying to find:
Opposite, Adjacent or Hypotenuse
• Step 2 Choose which trigonometric ratio to use:
• SOH CAH TOA
• Step 3 Substitute in the values in the formula
• Step 4 Solve the inverse trigonometric function
The inverse trigonometric function:
The sine takes the angle θ , give us the ratio:
sin(θ) = opposite⁄ hypotenuse
The inverse sine takes the ratio, give us the angle:
sin-1 (opposite/hypotenuse) =θ
For example:
sin (30) = 0.5 sin-1(0.5)=30
Similarly to cos and tan
Show students how to press the inverse trigonometric ratios in their calculator.
13:50-13:55
Example: Finding missing angle
Step 1 The two sides are involved are Opposite and Hypotenuse.
Step 2 SOH CAH TOA tells us to use sin
Step 3 Substitute in the values in the formula
sin (x) = opp/hyp = 2.5/5
Step 4 Solve equation
x = sin-1 ( 2.5/5 )
= sin-1 (0.5)
= 30
The measure of angle “ x “ is 30
!3:55-14:05
14:05-14:07
•
Two practice questions for finding missing angle
Conclusion: summary the steps for finding missing side and finding missing angle.
Assessment:
Students will be questioned throughout the lesson.
Students will be given two practice questions for each topic.
REFLECTION:
(on lesson)
PROFESSIONAL
COMPETENCIES
ADDRESSED: