9-1 Right triangle trig ratios Download

Transcript
Name ___________________________
9-1 Notes
IB Math SL
Lesson 9-1 Right triangle trigonometric ratios
Learning Goal: How can we use Trig Ratios in a right triangle to determine the length of a side or the angle in a right
triangle?
Today we will review triangle concepts you learned past math courses. We will be pair teaching and looping our
work!
#1 Loop Partner Work
Loop 1: Solving for sides of a right triangle
In your pairs the TEACHER will read the review notes and worked out examples. Then you will collaborate with
each other to solve the practice questions and check answers. Don’t forget to show all work.
Teacher Reads!
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A ratio is another way of saying a proportion or a fraction.
In Right triangles we often are interested in looking at the different sides of the triangle.
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The Sides of a Right Triangle
The hypotenuse is the longest side of a right triangle, the side opposite
of the right angle.
The opposite side or leg is opposite the given non-right angle.
The adjacent side or leg is next to the given non-right angle.
If we know one side of a right triangle and one angle we can often find one of the other 2 sides through the
use of trigonometric ratios!
Worked out example:
Try one together:
Work on this set of problems individually. DO NOT WORK WITH YOUR PARTNER until both of you are done
with this section. Once both partners are completed, check answers with me then move on to the next loops.
Do not progress without your partner.
1. As shown in the diagram below, a building casts a 72 foot shadow on the ground when the angle of elevation of the
Sun is 40°.
How tall is the building, to the nearest foot?
2. Find all unknown angles and sides, to 3 significant figures of:
3. IB QUESTION: The following diagram shows a sloping roof. The surface ABCD is a rectangle. The angle ADE is 55°. The
vertical height, AF, of the roof is 3 m and the length DC is 7 m.
B
C
A
7m
3m
55°
E
Calculate AD.
F
D
Loop 2: Solving for angles in a right triangle
In your pairs the TEACHER will read the review notes and worked out examples. Then you will collaborate with
each other to solve the practice questions and check answers. Don’t forget to show all work.
Teacher Reads!
Finding Angles Using SOH-CAH-TOA using inverse trig functions:
 To find angles () using Sine, Cosine, and Tangent you must perform the inverse of the trig function
 The inverse trig functions are represented as:
−  −  − 
 When using the inverse trig functions, you must be in degree mode in your calculator. ( 2ndtrig function)
Finding the angle of elevation or depression
Angle of elevation or depression is the angle between a horizontal line and the line joining a point of observation to
some object above or below the horizontal line.
Angle of elevation is always INSIDE the triangle, starting from the bottom!
Angle of depression is always OUTSIDE the triangle, starting from the top!
Worked out example:
Try together:
2. The diagram below shows the path a bird flies from the top of a 9.5 foot tall sunflower to a point on the ground
5 feet from the base of the sunflower.
To the nearest tenth of a degree what is the measure of angle x?
Work on this set of problems individually. DO NOT WORK WITH YOUR PARTNER until both of you are done
with this section. Once both partners are completed, check answers with me then move on to the next loops.
Do not progress without your partner.
1. A ladder is resting against the side of a building. The bottom of the ladder is 12 feet from the building, and the
ladder reaches 7 feet up the side of the building. Find the measure of the angle of elevation, to the nearest
tenth of a degree.
2. Solve for 
3. An observer stands 100 m from the base of a building. The angle of elevation of the top of the building is 65°. How
tall is the building, to the nearest meter?
Putting it all together! Work on these together!
1. IB Question: The diagram shows a cuboid 22.5 cm by 40 cm by 30 cm.
H
G
E
F
40 cm
D
C
30 cm
A
(a)
B
22.5 cm
Calculate the length of [AC]. (HINT: Pythagorean theorem!)
(b)
Calculate the size of GÂC . (Hint: Visualize the triangle that these 3 vertices create!)
2. IB QUESTION: The diagram shows a water tower standing on horizontal ground. The height of the tower is
26.5 m.
xm
A
a) From a point A on the ground the angle of elevation to the top of the tower is 28°. Label Angle A as 28°in the
diagram.
b) Calculate, correct to the nearest metre, the distance x m.