The document provides a lesson on solving right triangles using trigonometric ratios. It begins by reviewing the parts of a right triangle, including the legs and hypotenuse. It then defines the six trigonometric ratios using sine, cosine, tangent, cosecant, secant, and cotangent. Examples are provided to demonstrate determining the appropriate ratio to use when a right triangle has given and missing parts. Students are assessed on writing the correct formula to solve for missing parts in various right triangle scenarios.

1. Lesson Exemplar in Mathematics 9
Lesson: Solving Right Triangle by using Trigonometric Ratios
Grade Level: Grade 9
Grading Period: Fourth Quarter
Learning Competency:
Determining what formula/equation is needed in solving the missing part of a
right triangle.
Duration: 1 session
A. RECALL:
 Parts of a Right triangle
Questions:
What is called to perpendicular sides of a right triangle? Answer: legs
What is called to the slanting side of a right triangle? Answer: hypotenuse
 The Six Trigonometric Ratios
Questions:
 What is reference angle? Answer: It is an angle use to identify the specified
term for the legs of a right triangle, the opposite side and the adjacent side.
It may be θ, A, B or any capital letter of the English alphabet.
 How do you know the opposite side in a right triangle? Answer: It is the side
opposite the reference angle.
 How do you know the adjacent side in a right triangle? Answer: It is the side
adjacent to the refence angle other than the hypotenuse.
 What are the 6 trigonometric ratios? Answer: Sine θ, Cosine θ, Tangent θ,
Cosecant θ ,Secant θ and Cotangent θ.
 What is sine θ? Answer: sin θ = opposite/hypotenuse
 What is cosine θ? Answer: cos θ = adjacent/hypotenuse
 What is tangent θ? Answer: tan θ= opposite/adjacent
 What is cosecant θ? Answer: csc θ = hypotenuse/opposite
 What is cotangent θ? Answer: cot θ = adjacent / opposite
 What is secant θ? Answer: sec θ = hypotenuse/adjacent
 How do you find the measure of A, if sin A = 0.3456? Answer: Enter shift sin
0.3456
 What is the value of A ,if sin A = 0.3456? Answer: 20.220

2. c = 23a
b=17
B
C A

A = 42.34⁰
B = 47.66⁰ a = 15.49
CosA=
===
Cos A =
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 41⁰.
How far is the observer
from the base of the tower.
B.DISCUSSION:
To determine the trigonometric ratio use in solving the missing parts of a right triangle,
follow these steps:
a. Understand, analyze, then draw the triangle, if triangle is not yet drawn and
label it correctly.
b. Know what is the reference angle.
c. Identify the given parts and know what is to find for.
d. Choose the appropriate trigonometric ratio needed to solve the missing parts
of a right triangle.
Examples:
1. Triangle BCA is right- angled at C. If a=23 and b=17, find A, B and a. Express your
answer in two decimal places.
 Understand, then sketch the problem.
Reference angle: A or θ
opposite side: a=?
adjacent side: b=17
hypotenuse: c =23
Acute angles: A=? ,B=?
In solving A, the reference angle, use cosine since the given sides are adjacent and
hypotenuse.
adjacent side 17 A =cos-1 17
hypotenuse 23 23
Since mA + mB + mC = 180 in any triangle, therefore mB = 180- (mA + mC)
In finding a, there are two possible trigonometric ratios to use, either tangent or sine.
Using sin A = opposite side/hypotenuse; sin 42.35 = a/23
a = 23(sin42.35)
Using tan A= opposite/adjacent ; tan 42.35 = a/17
a=17(tan 42.35)
You will notice that the values of a are equal since we are referring to the same triangle, if
you try to find the value of a.
2.
B

3. Tan 410 =
A 410 C
X
or
opposite side 15.24
adjacent side X X=
𝟏𝟓.𝟐𝟒
𝑻𝒂𝒏 𝟒𝟏
C. ASSESSMENT
Write the formula needed in solving the missing parts of a right triangle for each
problems below.
A. For numbers 1 to 5, use the figure below
B
1. If a=5 and c=10,find the measure of A.
a c 2. If b=7 and c= 12,find the measure of A.
3. If a= 8 and b = 10, find the measure of A.
C A 4. If the measure of A =700 and c= 15, find a.
b 5. If the measure of B =630 and b= 15, find a.
B. From the top of a cliff 280m high, the angle of depression of a boat is 700. How far from
the base of the cliff is the boat?
RUBRICS:
Task: Writingthe formula that isneededtosolve the missingpartsof the righttriangle.
Points 3 1 0
Criteria The answeris correct. The answeris wrong. No attempttoanswer.
15.24m
Since 15.24 is opposite the given
angle,410
,andthe missingside isX, the
adjacentside, the trigonometricratioto
use istangent.Rememberthe
mnemonicsSOH-CAH-TOA.
Tan A=