Embed Size (px)
Citation preview
| 1 T r i m e s t e r 2 - P a g e
Warm Up – These triangles are similar. Find x and y.
Geometric Mean
Name:
Period:
Essential Question:
Geometric Mean
Example 1
You Try 1
Altitude Theorem
Example 2
You Try 2
Description: The ____________ ______ of two positive numbers a and b is the
number x such that
So, ________________.
Find the geometric mean between 2 and 50.
Find the geometric mean between 3 and 12
Description: The altitude of a right triangle creates _________ similar triangles.
Sketch:
Write a similarity statement identifying the three similar triangles in the figure.
Write a similarity statement identifying the three similar triangles in the figure.
| 2 T r i m e s t e r 2 - P a g e
Geometry Mean
Theorems
Example 3
Example 4
You Try 3
Summarize
#1 #2
Find d, e, and c.
Find x, y, and z.
Find x, y, and z.
| 3 T r i m e s t e r 2 - P a g e
Warm Up –
1) Find the geometry mean between 9 and 13.
2) Find the altitude a.
Pythagorean Theorem
Name:
Period:
Essential Question:
Pythagorean Thm.
Example 1
You Try 1
Converse
Pythagorean Thm.
Description: in a ___________ triangle, the sum of the squares of the legs is equal
to the square of the ________________.
Find x.
Solve for x.
Description: we can classify if a triangle is acute, obtuse or right.
___________ triangle.
___________ triangle.
___________ triangle.
| 4 T r i m e s t e r 2 - P a g e
Example 2
You Try 2
Summarize
State if each triangle is acute, obtuse, or right.
State if each triangle is acute, obtuse, or right.
| 5 T r i m e s t e r 2 - P a g e
Warm Up –
1) Find x.
2) Is the a triangle with side lengths 3, 7,
and 9 acute, obtuse or right?
Special Right Triangles
Name:
Period:
Essential Question:
- -
Example 1
You Try 1
Description: the legs ___ are congruent and the length of the hypotenuse ___ is
_____ times the length of the leg.
Find the value of x.
Find the value of x.
| 6 T r i m e s t e r 2 - P a g e
Example 2
You Try 2
Summarize
Find the value each variable.
Find the value each variable.
| 7 T r i m e s t e r 2 - P a g e
Warm Up - Find the hypotenuse u and the other leg v.
Special Right Triangles
Name:
Period:
Essential Question:
- -
Example 1
Example 2
Example 3
Description: the hypotenuse (___) is ____ times the shorter leg (___) and the
longer leg (___) is ____ times the length of the shorter leg.
Find m and n.
Find u and v.
Find a and b.
| 8 T r i m e s t e r 2 - P a g e
Example 4
You Try 1
You Try 2
You Try 3
Summarize
Find u and v.
Find x and y.
Find m and n.
Find x and y.
| 9 T r i m e s t e r 2 - P a g e
Warm Up – Find x and y.
Trigonometry A
Name:
Period:
Essential Question:
Sine
Cosine
Tangent
Example 1
You Try 1
Description: The ratio of the opposite leg and hypotenuse
Description: The ratio of the adjacent leg and hypotenuse
Description: The ratio of the opposite leg and adjacent leg
Find the value of each trigonometric ratio. SOH CAH TOA
sin
cos
tan
Find the value of each trigonometric ratio. SOH CAH TOH
sin sin
cos cos
tan tan
| 10 T r i m e s t e r 2 - P a g e
Example 2
Example 3
Example 4
You Try 2
Summarize
Find the missing side. Round to the nearest tenth. SOH CAH TOA
Find the missing side. Round to the nearest tenth. SOH CAH TOA
Find the missing side. Round to the nearest tenth. SOH CAH TOA
Find the missing side. Round to the nearest tenth. SOH CAH TOA
| 11 T r i m e s t e r 2 - P a g e
Warm Up – Use trigonometry to solve for x. SOH CAH TOA
Trigonometry B
Name:
Period:
Essential Question:
Inverse Functions
Sine Inverse
Cosine Inverse
Tangent Inverse
Example 1
Example 2
Example 3
Description: We can find the missing angles of a right triangle using just two sides
of a triangle.
(
)
(
)
(
)
Use a calculator to find the measure of P to the nearest tenth.
Find the measure of the indicated angle to the nearest degree.
Find the measure of the indicated angle to the nearest degree.
| 12 T r i m e s t e r 2 - P a g e
Example 4
You Try 1
You Try 2
Summarize
Find the measure of the indicated angle to the nearest degree. SOH CAH TOA
Find the measure of the indicated angle to the nearest degree.
Find the measure of the indicated angle to the nearest degree.
| 13 T r i m e s t e r 2 - P a g e
Warm Up - 1) Use a calculator to find
2) Find x. Round to the nearest tenth.
Angles of Elevation and
Depression
Name:
Period:
Essential Question:
Angle of Elevation
Angle of Depression
Example 1
Example 2
Example 3
Description: angle formed when ___________ ____.
Description: angle formed when ___________ _______.
Name the angle of depression and angle of elevation in each figure
Elev: Elev:
Dep: Dep:
SHADOWS Suppose the sun casts a shadow off a 35-foot building. If the angle of
elevation to the sun is 60°, how long is the shadow to the nearest tenth of a foot?
RESCUE A hiker dropped his backpack over one side of a canyon onto a ledge
below. Because of the shape of the cliff, he could not see exactly where it landed.
From the other side, the park ranger reports that the angle of depression to the
backpack is 32°. If the width of the canyon is 115 feet, how far down did the
backpack fall? Round your answer to the nearest foot.
| 14 T r i m e s t e r 2 - P a g e
You Try 1
You Try 2
You Try 3
Summarize
LIGHTHOUSES Sailors on a ship at sea spot the light from a lighthouse. The
angle of elevation to the light is 25°. The light of the lighthouse is 30 meters above
sea level. How far from the shore is the ship? Round your answer to the nearest
meter.
SUN Find the angle of elevation of the Sun when a 12.5-meter-tall telephone pole
casts an 18-meter-long shadow.
CONSTRUCTION A roofer props a ladder against a wall so that the top of the
ladder reaches a 30-foot roof that needs repair. If the angle of elevation from the
bottom of the ladder to the roof is 55°, how far is the ladder from the base of the
wall? Round your answer to the nearest foot.
| 15 T r i m e s t e r 2 - P a g e
Warm Up – Name the angle of depression and elevation.
Law of Sines
Name:
Period:
Essential Question:
Law of Sine
Example 1
You Try 1
Description: If ∆ABC has lengths a, b, c, representing the lengths of the sides
opposite the angles with measures A, B, and C, then
Find p. Round to the nearest tenth.
Find c to the nearest tenth.
| 16 T r i m e s t e r 2 - P a g e
Example 2
You Try 2
Summarize
Find x. Round to the nearest tenth.
Find x. Round to the nearest degree.
| 17 T r i m e s t e r 2 - P a g e
Warm Up - Use law of sine to find AB.
Law of Cosine
Name:
Period:
Essential Question:
Law of Cosine
Example 1
You Try 1
Description: If ∆ABC has lengths a, b, c, representing the lengths of the sides
opposite the angles with measures A, B, and C, then
Find x. Round to the nearest tenth.
Find r if s = 15, t = 32, and mR = 40. Round to the nearest tenth.
| 18 T r i m e s t e r 2 - P a g e
Example 2
You Try 2
Summarize
Find mL. Round to the nearest degree.
Find mP. Round to the nearest degree.
