Transcript 5-4 Applying Trigonometric Functions

5-4 Applying Trigonometric
Functions
Objective: Use trig to find the
measures of the sides of right
triangles.
Meet Sam. Hi Sam!
Sam has a dilemma.
His cat Cuddles is stuck up a 30 foot tree.
Sam hears it’s safest to angle his ladder at
57o34’
1) How long must he extend his ladder?
2) How far away from the tree base should
he place his ladder?
1) How long must he extend his ladder?
• What do we know?
• What part of the
triangle is the ladder?
2) How far away from the tree base should
he place his ladder?
• Which side represents
the distance from base of
ladder to base of tree?
• Which trig function should
we use?
Now that Cuddles is safe,
A little more basic…
• If J = 50o and j = 12, find r.
(J is angle, little j is side across from angle)
G
12
r
50o
R
g
J
Using Trig with Other Shapes
• Find the apothem
(measure of a line
segment from the
center of the
polygon to the
midpoint of one of
its sides)
d = 26.6 inches
d = 23.4 inches
r=
a=
When in doubt, look for right triangles!
Angles of Elevation and
Depression
• What do you think of
when you think of
“elevation”?
• “Depression”?
An angle of elevation is the angle between a
horizontal line and the line of sight from an
observer to an object at a higher level.
An angle of depression is the angle between
a horizontal line and the line of level.
The angles of elevation and depression are
equal in measure because they are alternate
interior angles.
Turn to Page 301 to Follow Along
On May 18, 1980, Mount Saint Helens, a volcano
in Washington, erupted with such force that the
top of the mountain was blown off. To determine
the new height at the summit of Mt. St. Helens, a
surveyor measured the angle of elevation to the
top of the volcano to be 37o46’. The surveyor
then moved 1000 feet closer to the volcano and
measured the angle of elevation to be 40o30’.
Determine the new height of Mt. St. Helens.
Use Tangent Function to create two
equations.
Extra work from volcano problem.
Homework
• Pg 302-303 #10-18e, 20, 26, 30, 31
Practice 5.4