Lesson 25A M2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name_______________________
Date________________
Period ________
Lesson 25A: Using Trig Ratios to Find Missing Sides
Learning Targets

I can use the trig ratios to find the missing lengths of sides

I can use the graphing calculator to find the values of sin⁡(𝜃) , cos⁡(𝜃) and tan⁡(𝜃) for 𝜃 between 0° and 90°.
Opening exercise
Given the triangle identify the following Trig Ratios
sin(𝐴) =
𝑠𝑖𝑛(𝐵) =
𝑐𝑜𝑠(𝐴) =
𝑐𝑜𝑠(𝐵) =
tan(𝐴) =
𝑡𝑎𝑛(𝐵) =
Be Aware:
We use CAPITAL letters to represent angle measurements, and the same letters in lower case to represent
the side measurements opposite those angles. We also use the theta symbol θ to represent angle measures.
Exploratory Challenge:
How do we find sine, cosine, and tangent of a given angle?
Use a calculator to find the sine, cosine, and tangent of 𝜽. Give your answer
rounded to the ten-thousandth place, i.e. 𝑋. 𝑋𝑋𝑋
𝜽
𝐬𝐢𝐧 𝜽
𝐜𝐨𝐬 𝜽
𝐭𝐚𝐧 𝜽
𝟎
𝟐𝟎
𝟑𝟎
𝟒𝟎
𝟓𝟎
𝟔𝟎
𝟕𝟎
𝟗𝟎
Lesson 25A M2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name_______________________
Date________________
Period ________
How we can use the trig ratios to find the lengths of the missing sides?
Basic Trigonometric Functions (SOH – CAH – TOA)
To Find a Missing Side/Angle:
1. Pick the right equation relative to the angle and sides given
2. Substitute variables and values into the trig function.
3. Cross-multiply to solve
Problem
Example 1
Math explanation
Find the value of 𝑎
Example 2
Find the value of 𝑏
Find the value of ℎ
Example 3
Draw the picture
Find the length of 𝐴𝐵 to the nearest
integer
In right triangle ABC, 𝑚∠𝐶⁡ = ⁡90° ,
𝑚∠𝐴⁡ = ⁡47°, and 𝐶𝐴⁡ = ⁡19.
Math explanation
Find the value of 𝑏
Lesson 25A M2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name_______________________
Date________________
Period ________
Lesson 25A: Using Trig Ratios to Find Missing Sides
Classwork
Exercises 1–3 (10 minutes)
Find all the unknown lengths. Approximate your answers to one decimal place.
Note : The answers are approximations because the acute angles are really only approximations, not exact measurements.
1.
2.
3.
𝑥 = _______________
𝑥 = _______________
𝑥 = _______________
𝑦 = _______________
𝑧 = _______________
𝑧 = _______________
4. From a point 120⁡m away from a building, Serena measures the angle between the ground and the top
of a building and finds it measures 41˚. What is the height of the building? Round to the nearest
meter.
𝑧
5. Use the chart from the Exploratory Challenge to approximate the unknown lengths 𝑦 and 𝑧 to one
decimal place.
°
Lesson 25A M2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name_______________________
Date________________
Lesson 25A: Using Trig Ratios to Find Missing Sides
Homework
For each problem, approximate the unknown lengths to one decimal place.
1. Find the approximate length of the leg opposite the 𝟖𝟎° angle.
2. Find the approximate length of the hypotenuse.
3. Find the approximate length of the hypotenuse.
4. Find the approximate length of the leg adjacent to the 𝟒𝟎° angle.
Period ________
Lesson 25A M2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name_______________________
Date________________
5. Find the length of both legs of the right triangle below. Indicate which
leg is adjacent and which is opposite the given angle of 𝟑𝟎°.
6. ****Three city streets form a right triangle. Main Street and
State Street are perpendicular. Laura Street and State Street
intersect at a 𝟓𝟎° angle. The distance along Laura Street to
Main Street is 𝟎. 𝟖 mile. If Laura Street is closed between
Main Street and State Street for a festival, approximately
how far (to the nearest tenth) will someone have to travel to
get around the festival if they take only Main Street and
State Street?
7. A cable anchors a utility pole to the ground as shown in the
picture. The cable forms an angle of 𝟕𝟎° with the ground.
The distance from the base of the utility pole to the anchor
point on the ground is 𝟑. 𝟖 meters. Approximately how long
is the support cable?
Period ________