textbook: chapter 13. make sure that your calculator is set to the proper mode

UNIT 8: TRIGONOMETRY

Textbook: Chapter 13

Assignment Sheet

** Make sure that your calculator is set to the proper mode**

Parts Of A Right Triangle

Leg

Hypotenuse

Leg

Right Angle

AcuteAngles

13.1 Special Right Triangles

The Pythagorean TheoremIn a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

“No man is free who cannot control himself.” ― Pythagoras of Samos



Pythagorean Theorem(leg)2 + (leg)2 = (hypotenuse)2 or a2 + b2 = c2

E1.) a = 3, b = 4 and c = ? P1.) a = 5, b = ? and c = 13

E2.) a = ? , b = 36 and c = 39 P2.) a = 7, b = and c = ?

E3.) a = , b = ? and c = 12 P3.) a = ?, b = 3 and c =


The sides of special right triangles (45-45-90 and 30-60-90) have special relationships (ratios)

Given one side of a certain right triangle, we can use these relationships (ratios) to unlock the other two sides.

Why is this important if we already know the Pythagorean Theorem?We must know 2 sides of a right triangle to use the Pythagorean Theorem.


45-45-90

If you are given a:Leg (S)

The other leg is the same Multiply by to find the L (hypotenuse)

Hypotenuse (L) Divide by to find the S (legs)


b = c =

a = b =

a = b =


30-60-90

If you are given a:Small Leg (S)

Multiply S by to find M Multiply S by 2 to find L

Medium Leg (M) Divide M by to find S Multiply S by 2 to find L

Hypotenuse (L) Divide L by 2 to find S Multiply S by to find M

*You need the S to unlock the M and L*


b = c =

a = b =

a = b =

TrigonometryTrigonometry – measurement of triangles

Trigonometry Vocabulary-based on the acute angle ( that is being

usedFrom From

OppositeHypotenuse

Adjacent Opposite

Adjacent Hypotenuse

13.1 Sine, Cosine and Tangent

Trigonometric Ratio – a ratio of the lengths of two sides of a triangle.

Sine (sin), Cosine (cos) and Tangent (tan) are the 3 basic trigonometric ratios

TanSin Cos


Solving Trigonometric Equations

E1) Variable on top (multiply both sides by the denominator)

E2) Variable on bottom (flip-flop the trig function and the variable)

E3) Variable attached to the trigonometric function (inverse both sides)


Solving Trigonometric EquationsP1) Variable on top (multiply both sides by the denominator)

P2) Variable on bottom (flip-flop the trig function and the variable)

P3) Variable attached to the trigonometric function (inverse both sides)



45

5 3543

65

2565

=513

6065

=1213

2560

=512


O

H

O

A

𝑆𝑜h𝐶𝑎h𝑇 𝑜𝑎


A

H

𝑆𝑜h𝐶𝑎h𝑇 𝑜𝑎

Solving a right triangle means to find the measure of three angles of the triangle and three sides of the triangle. In other words all six parts.

You can solve a right triangle if you know:(1) Two side lengths OR(2) One side length and one angle measure



A= a=B= b=C= c=949 °

90 ° 11.9

7.841° Step 1: Find a missing side using the given information (Find c)

B,b,c

Step 2: Find the other side (Find a)B,b,a


A= a=B= b=C= c=90 °62 ° 31′27 ° 29′ 6

1311.5 Step 1: Find the missing Side

Step 2: Find a missing angle using the given information (Find A)

A,a,c


B,a,c

Angle of Elevation vs. Angle of Depression

Angle of Elevation = Angle of Depression


Angle of Elevation vs. Angle of DepressionYou are standing on top of a building that is 50 ft. tall and you see your buddy on the street. He is standing 30 ft. from the base of the building. Find the angle of depression between you and your buddy.

The angle of elevation is 59° and because the angle of elevation is the same as the angle of depression, then the angle of depression is also 59°.



60 ft65 °

𝑥


175 ft

200 ftAngle of Depression𝜃

textbook: chapter 13. ** make sure that your calculator is set to the proper mode**

Documents

textbook: chapter 13. make sure that your calculator is set to the proper mode