Download Lesson 7-2: Using Trigonometric Functions to

Geometry/Trig
Name: __________________________
Date: ______________________
Lesson 7-2: Using Trigonometric Functions to Solve for Sides
Learning Goal: #2- What are trigonometric ratios and how can we use them to solve for a side?
HOW TO REMEMBER THE TRIG RATIOS!
Let’s Warm-Up with a “Level 2!”
The diagram below shows right triangle UPC. Which ratio represents the Cosine of ∠𝑈?
Solving for a Side Using Trigonometric Ratios
1. In right triangle ABC, hypotenuse AB=15 and angle A=35º. Find leg length, BC, to the nearest tenth.
Why CAN’T we use Pythagorean Theorem here??
So, what can we use?
1. Draw your diagram and
label all parts of the
triangle.
2. Ask yourself, what sides
and angles are
“involved?”
3. Choose your trig ratio
using SohCahToa.
4. Solve for x and answer
the question!
Geometry/Trig
Let’s try another!
2. In right triangle ABC, leg length BC=20 and angle B = 41˚. Find hypotenuse length BA to the nearest hundredth.
1. Draw your diagram and
label all parts of the
triangle.
2. Ask yourself, what sides
and angles are
“involved?”
3. Choose your trig ratio
using SohCahToa.
4. Solve for x and answer
the question!
You Try!
3. In the right triangle shown in the diagram below, what is the value of x to the nearest whole number?
1. Draw your diagram and
label all parts of the
triangle.
5. Ask yourself, what sides
and angles are
“involved?”
6. Choose your trig ratio
using SohCahToa.
7. Solve for x and answer
the question!
Geometry/Trig
Tips for Success
1) Always draw a diagram and carefully label
2) There are two descriptions of angles that can be given in problems:
a) Angle of Elevation
b) Angle of Depression
*Angle of elevation and angle of depression are _____________ through ______________________________________
3) ALWAYS round your answer at the end. The ONLY thing you should round is your FINAL ANSWER
Practice Time with LEVEL
3’s!
4. In the accompanying diagram, a ladder learning against a building makes an angle of 58° with level ground.
If the distance from the foot of the ladder to the building is 6feet, find, to the nearest foot, how far up the
building the ladder will reach.
Geometry/Trig
5. The accompanying diagram shows a ramp 30 feet long leaning against a wall at a construction site. The
ramp makes a 32° angle with the ground. How tall is the wall to the nearest foot?
6. A ramp is leaning against a wall. The angle the ramp makes with the ground is 18°. The length of the ramp
is 12 feet. Find the length from the bottom of the ramp to the wall to the nearest hundredth of a foot.
Geometry/Trig
LEVEL 4
You may want to redraw triangles if there are more than one in the picture!
11. As shown in the diagram below, a ship is heading directly toward a lighthouse whose beacon is 125 feet
above sea level. At the first sighting, point A, the angle of elevation from the ship to the light was 7°. A
short time later, at point D, the angle of elevation was 16°. Determine the distance from A to D,to the
nearest 10th.
HINT! Label your diagram each time you find an answer!
Geometry/Trig
Name: __________________________
Lesson 7-2: Homework
1. From a point on level ground 25 feet from the base of a tower, the angle of elevation to the
top of the tower is 78°, as shown in the accompanying diagram. Find the height of the tower,
to the nearest tenth of a foot.
2. The tailgate of a truck is 2 feet above the ground. The incline of a ramp used for loading the truck is 11°, as
shown below.
Find to the nearest tenth of a foot, the length of a the ramp.
Geometry/Trig
3. A 10-foot ladder is to be places against the side of a building. The base of the ladder must be places at an
angle of 72° with the level ground for a secure footing. Round all answers to the nearest 10th.
a. Find how far the base of the ladder should
b. Find how far up the side of the
be from the side of the building
building the ladder will reach.
10.
a) Find the length of CA, to the nearest whole number.
HINTS!
1) Label your diagram each time you find an answer!
2) You may want to redraw triangles if there are
more than one in the picture!
b) Using your answer form part (a) find the length of
BC to the nearest whole number.
c) Using your answer form part (b), find the length of DC to the nearest whole number.
Geometry/Trig