Transcript More Practice with the Trigonometric Functions

More Practice with
the Trigonometric
Functions
Section 4.2b
Applications of Right Triangle
Trigonometry
How many “parts” are in every triangle?
Six  3 angles and 3 sides
If we have any three of these parts, we can usually
find the other three…
This process is called solving a triangle.
Solving Right Triangles
A right triangle with a hypotenuse of 8 includes a 37 degree
angle. Find the measures of all of the other parts of the
triangle.
First, the missing angle:
Start with a diagram:
180 – 90 – 37 = 53
sin 37 
8
37
a
b
b
8
Use trig. to find the other sides:
b  4.815
b  8sin37
a
37 
acos
 6.389
8
a  8cos37
Solving Right Triangles
Use the given information to completely solve the triangle.
  41
B

a
c  10
c

C
b
a  6.561
A
b  7.547
  49
Solving Right Triangles
Use the given information to completely solve the triangle.
a 5
B

a
  59
c

C
b
b  8.321
A
c  9.708
  31
Solving Right Triangles
From a point 340 feet away from the base of Peachtree Center
Plaza in Atlanta, GA, the angle of elevation to the top of the
building is 65 . Find the height h of the building.
The diagram?
h
65
340 ft
h
tan 65 
340
h  340 tan 65
h  729.132
feet
Whiteboard Problems
Kirsten places her surveyor’s telescope on the top of a tripod 5 ft
above the ground. She measures an 8 degree elevation above the
horizontal to the top of a tree that is 120 ft away. How tall is the
tree?
h  21.865
feet
Whiteboard Problems
A climber falls from the top of a cliff and is stuck on a ledge some
distance off the ground. A rescue party is currently 1200 ft from
the base of the cliff, and spots the climber and the top of the cliff
at angles of 55 and 62 , respectively. How far did the climber
fall?
d  543.094 feet