Download Name: TP: ______ CRS CLASS OF 2015 AVERAGE MASTERY

CW#77: Pythagorean, Special Right Triangles, Trig
Geometry
Name: ________________________________ TP: _______
CRS
CLASS OF 2015 AVERAGE MASTERY
PPF602: Use the Pythagorean Theorem
51%
PPF601: Apply properties of 30-60-90, 45-45-90, similar,
and congruent triangles
48%
FUN 502 Express sine, cosine, and tangent of an angle in
a right triangle as a ratio of given side lengths
46%
FUN602: Apply basic trigonometric ratios to solve righttriangle problems.
56%
HOW DO YOU STACK UP?!
FISCHER
MASON/YOUNG
WALDEN/ZIEGLER
1ST
X
57%
X
3RD
X
4TH
X
X
5TH
53%
X
58%
HOW DO WE STACK UP?!
Campus
Rauner
Golder
UIC
Noble
Muchin
Percent Mastery
66%
63%
61%
58%
58%
Place
1
2
3
4
4
YOU ALL TRYING TO BE FOURTH PLACE?!
We didn’t think so…
Get your TEAMS in gear…
Get hyped…
It’s time to PUSH IT TO THE LIMIT.
You re-take the interim in ____ days.
Today, I commit to: __________________________________________________________________________________________________
_________________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________.
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INDEPENDENT REFLECTION: Write down everything you know about standard PPF602: Use
Pythagorean Theoreom.
Find the area of the triangle. Leave your answer in simplified radical form.
1)
2)
Determine if the following triangles are right triangles. Triangles are right triangles if Pythagorean
Theorem holds true.
4)
3) Sides: 3, 4, 5
5) The top of a ladder rests against a wall, 23 feet
above the ground. The base of the ladder is 6 feet
away from the wall. What is the length of the
ladder?
6) In rectangle MNLO below, how much longer is
the perimeter than the diagonal ML?
M
24 m
N
18 m
O
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L
7) A rectangular field shown below is 60 feet wide
and 40 feet long. Alissa and Bianca are at point B.
Alissa walks to point C by walking along the edge of
the field through point A. Bianca walks to point C
by walking diagonally across the field. To the
nearest whole, how many meters more does Alissa
walk than Bianca?
8) One route along flat terrain from Madison to
South Bend is to drive south from Madison for 400
miles to Chicago, then at Chicago to drive east 500
miles to South Bend. If a straight flat road existed
between Madison and South Bend, how many miles
would it be?
Madison
A
B
Chicago
C
South Bend
D
INDEPENDENT REFLECTION: Write down everything you know about standard PPF601: Apply properties
of 30-60-90, 45-45-90, similar, and congruent triangles.
9) Find the value of each variable. Write answers
in the simplest radical form.
10) Triangle CDE is a right triangle. The measure of
CED is 45 degrees, and the length of CE is 22 inches.
What is the length of CD?
C
D
E
11) Triangle ABC is a right triangle. The measure of 12) What is the perimeter of the triangle below?
ABC is 45 degrees, and the length of the hypotenuse
is 6. What is the length of one of the legs?
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13) In a 30-60-90, the shortest leg has a measure of
10 yards. What is the value of the perimeter?
14) In a 30-60-90 triangle, the hypotenuse has a
measure of 20 inches. What is the value of the
perimeter?
INDEPENDENT REFLECTION. Write down everything you know about FUN 502 Express sine, cosine,
and tangent of an angle in a right triangle as a ratio of given side lengths, and FUN602: Apply basic
trigonometric ratios to solve right-triangle problems.
15) Find each trigonometric ratio for the given
right triangle.
A
sin A = ______
b
cos A = ______
tan A = ______
sin C = ______
c
C
B
a
16) Find each trigonometric ratio for the given
right triangle.
sin A = ______
cos A = ______
tan A = ______
A
13
5
C
B
12
sin B = _______
cos C = ______
cos B = ________
tan C = _______
tan B = _______
17) An angle in a right triangle has a measure of β.
36
If tan β = 15 , then sin β = ?
18) An angle in a right triangle has a measure of Φ.
3
If cos Φ = 5 , what is sin Φ ?
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19) An angle in a right triangle has a measure . If
8
tan = 15 , then sin = ?
20) An angle in a right triangle has a measure of
5
If sin
= 13 , what is cos
?
21) In the figure below, ABC is a right triangle
with a right angle at C. Which of the statements
about this figure is NOT correct? Label sides A, O, H.
22) You are at the top of a roller coaster 100 feet above
a. cos A =
3
5
.
the ground. The angle of depression is 44°. What is the
distance x?
A
5
3
4
5
b. sin A =
3
c. tan A =
4
d. cos B =
C
4
B
4
5
3
4
23) A lamppost if 11 feet tall. If the angle of
elevation is 49 degrees. Which of the following is a
trig ratio that could be used to find x? Solve for x.
x
A. sin 49 
11
tan B =
24) A lamppost, shown below, casts a 10ft. shadow
when the sun is at a 60° angle with the ground.
Which of the following would give the height of the
lamppost? What is the height to the nearest whole?
tan 10
60
tan 60
B.
10
C. 60 tan 10
D. 10 tan 60
A.
x
B. cos 49 
11
C. sin 11 
49
x
D. sin 49 
11
x
E. tan 49 
11
x
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25) To calculate the height h of a flagpole, you
move 22 feet from the base and record the angle of
elevation to the top to be 65°. Find the flagpole's
height to the nearest foot.
26) A staircase has an angle of elevation of 28° and
covers a total distance of 17ft. To the nearest foot,
what is the vertical height h covered by the
staircase?
27) The angle of elevation from the base to the top
of a water slide is about 28°. The horizontal length
of the slide is about 45 feet. Find the height h of the
slide to the nearest whole.
28) You lean a 16 foot ladder against the wall. If the
ladder makes an angle of 70° with the ground, how
far away from the wall is the base of the ladder?
Round your answer to the nearest tenth of a foot.
29) You are standing near the Washington
Monument which is 555 feet tall. The angle of
elevation from your position to the top of the
monument is 45°. How far are you from the
monument?
30) You are using a ladder to paint the side of a
building. If you place the ladder 4 feet away from
the wall, with an angle of elevation of 75.5 degrees.
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Name: _______________________________ TP: _____
EXIT SLIP
Score: ______ / 2
1)
2)
3) Reflect in complete sentences.
A) What do all of the standards we learned about today have in common?
B) When do you use Pythagorean Theorem?
C) When do you use trigonometric ratios (SOHCAHTOA)?
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CHALLENGE You are traveling along a stretch of highway that has a slight grade with an angle of
inclination of 5°. After traveling for 4 miles, what is the vertical v and horizontal h change in feet? (1 mi =
5280 ft). Round your answer to the nearest foot.
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