Transcript 8.3: Right Triangle Trigonometry

3.2a: Right Triangle
Trigonometry
CCSS:
G-SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles
in the triangle, leading to definitions of trigonometric ratios for acute angles.
G-SRT.7 Explain and use the relationship between the sine and cosine of complementary
angles.
G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in
applied problems.?
GSE’s Covered
M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments,
uses geometric properties, or uses theorems to solve problems involving angles,
lines, polygons, circles, or right triangle ratios (sine, cosine, tangent)
within mathematics or across disciplines or contexts
(e.g., Pythagorean Theorem, Triangle Inequality Theorem).
Reference angle- an
acute angle used in
the right triangle
Using the reference angle for the right triangles above, identify: adjacent side, opposite side, hypotenuse.
All are sides of right triangles
SOHCAHTOA
opp
sin( ref angle) 
hyp
Replace
this
With either
the angle
Or variable
adj
cos(ref angle) 
hyp
opp
tan(ref angle) 
adj
What does it mean?
opp
sin( refangle) 
hyp
The sine of the reference angle is the ratio of the opposite side to the hypotenuse
of a right triangle.
The angle we are talking about
9 in
8 in
The opposite side to the angle we are
talking about
x
So, sin x =
8
9
Lets solve this equation
Always the
hypotenuse in a
right triangle
opp
sin x 
hyp
C
x
A
10
in
4
in
4
sin x 
10
To solve for the angle, we
need to get rid of sin
B
To get rid of sin and
solve for the angle we
1
use sin on both sides
4
sin x 
10 1 4
1
(sin ) sin x  (sin )
10
x  sin 1
4
10
x  24
Which means the angle is about 24
degrees
Reference angle
Solve for x
Label the information you have in the triangle
50
Adjacent
Side to 6 in
The ref
angle
x
6
cos 50 
x
6
( x) cos 50  ( x)
x
( x) cos 50  6
6
( x) 
cos 50
hypotenuse
If we have the Adjacent side and the
Hypotenuse, think SOHCAHTOA
Now solve
For x
adj
cos x 
hyp
Multiple both sides
by x
Divide both sides by
Cos 50
x  9.33in
Which means the hypotenuse is 9.3 in
Adjacent side to the ref
angle
8 ft
Solve for x
Label the information you have in the triangle
70
X ft
Opposite side to
the ref angle
opp
tan x 
adj
x
tan 70 
8
x
(8) tan 70  (8)
8
(8) tan 70  x
x  22 ft
If we have the Opposite side and the
Adjacent, think SOHCAHTOA
Multiply both sides by 8
You have x alone, so evaluate 8 tan 70
So the opposite side is approximately 22 ft
Primary: M(G&M)–10–2
Secondary: M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance,
midpoint, perpendicular and parallel lines, or slope.
Example on the coordinate plane
C (7,9)
B (4,5)
A (8,2)
Find mC in ABC
Solve for the missing sides of the triangle using 2 different methods. Show all work
NECAP released Item 2007
Find the area of the triangle
Find the Volume of the Prism
Phil stands on the sidewalk of a road. Phil’s favorite pizza restaurant is on the
other side of the road. His estimated line of sight to the pizza place is 43
degrees. He needs to go to the post office at some point which is 120 feet up
the road he is standing on. The line of sight from the post office to the pizza
place is 90 degrees.
How far of walk would it be for Phil from his original position to the pizza
place?
How far is the walk from the post office to the pizza place?
Homework