Common Core Geometry
Final Exam Review
Name _________________________________________
Date ___________________ Period ______________
Trig Review
Opening Exercise
1.
Find the exact value of x:
2.
Find x to the nearest tenth:
3.
Find x to the nearest degree.
Pythagorean Theorem

Used when working with 3 sides of a right triangle.

Formula:
Basic Trig Ratios

Used when working with an angle of a right triangle.

sinq =
Hypotenuse is always across from the
right angle.
cosq =
Opposite side is across from the angle
you are working with.
tanq =
Adjacent side is next to the angle you
are working with.

To find a missing angle, set up the trig ratio and use arcsin, arccos or arctan ( sin -1 q ,
cos-1 q or tan-1 q .
Exercises
1.
In
, the measure of
,
Which ratio represents the sine of
?
,
, and
.
1)
2)
3)
4)
2.
In the accompanying diagram of right triangle ABC,
,
, and
. What is
?
,
3.
In the right triangle shown in the diagram, what is
the value of x to the nearest whole number?
4.
An 8-foot rope is tied from the top of a pole to a stake in the ground, as shown in the
diagram pictured.
If the rope forms a 57° angle with the ground, what is the
height of the pole, to the nearest tenth of a foot?
5.
A hot-air balloon is tied to the ground with two taut (straight) ropes, as shown in the
diagram below. One rope is directly under the balloon and makes a right angle with
the ground. The other rope forms an angle of 50º with the ground.
a.
Determine the height, to the nearest
foot, of the balloon directly above the
ground.
b.
Determine the distance, to the nearest
foot, on the ground between the two
ropes.
6.
In right triangle ABC,
inches,
inches, and
. Find the
number of degrees in the measure of angle BAC, to the nearest degree.
7.
A communications company is building a 30-foot antenna to carry cell phone
transmissions. As shown in the diagram below, a 50-foot wire from the top of the
antenna to the ground is used to stabilize the antenna.
Find, to the nearest degree, the measure of the angle that the wire makes with the
ground.
8.
As seen in the accompanying diagram, a person can travel
from New York City to Buffalo by going north 170 miles to
Albany and then west 280 miles to Buffalo.
If an engineer wants to design a highway to connect New
York City directly to Buffalo, at what angle, x, would she need
to build the highway? Find the angle to the nearest degree.
Angles of Elevation & Depression
1.
A person measures the angle of depression from the top of a wall to a point on the
ground. The point is located on level ground 62 feet from the base of the wall and
the angle of depression is 52°. How high is the wall, to the nearest tenth of a foot?
2.
A man standing on level ground is 1000 feet away from the base of a 350-foot-tall
building. Find, to the nearest degree, the measure of the angle of elevation to the top
of the building from the point on the ground where the man is standing.
Trig Review – Day 2
Opening Exercise
A man who is 5 feet 9 inches tall casts a shadow of 8 feet 6 inches. Assuming that the man
is standing perpendicular to the ground, what is the angle of elevation from the end of the
shadow to the top of the man’s head, to the nearest tenth of a degree.
More Practice
As shown below, a canoe is approaching a lighthouse on the coastline of a lake. The front of
the canoe is 1.5 feet above the water and an observer in the lighthouse is 112 feet above
the water.
At 5:00, the observer in the lighthouse measured the angle of depression to the front of the
canoe to be 6° . Five minutes later, the observer measured and saw the angle of depression
to the front of the canoe had increased by 49° . Determine and state, to the nearest foot per
minute, the average speed at which the canoe traveled toward the lighthouse.
Sine and Cosine of Complementary Angles

If α and β are complementary angles then, sin α = cos β.
Practice Problems
1. In right triangle 𝐴𝐵𝐶 with right angle at 𝐶, sin 𝐴 = 2𝑥 + 0.1 and cos 𝐵 = 4𝑥 − 0.7.
Determine and state the value of 𝑥. Explain your answer.
2. Explain why cos(𝑥) = sin(90 − 𝑥) for 𝑥 such that 0 < 𝑥 < 90.
3.
In right triangle 𝐴𝐵𝐶, 𝑚∠𝐵 ≠ 𝑚∠𝐶. Let sin 𝐵 = 𝑟 and cos 𝐵 = 𝑠. What is sin 𝐶 −
cos 𝐶?
(1) 𝑟 + 𝑠
(2) 𝑟 − 𝑠
(3) 𝑠 − 𝑟
𝑟
(4) 𝑠
More Practice
1.
The circular frame of a Ferris wheel is suspended so that it sits 4 ft. above the
ground and has a radius of 30 ft. A segment joins center C to point S on the circle. If
̅̅̅
CS makes an angle of 48° with the horizon, what is the distance of point S to the
ground?
Horizontal Center Line
2.
An archaeological team is excavating artifacts from a sunken merchant vessel on the
ocean floor. To assist the team, a robotic probe is used remotely. The probe travels
approximately 3,900 meters at an angle of depression of 67.4 degrees from the
team’s ship on the ocean surface down to the sunken vessel on the ocean floor. The
figure shows a representation of the team’s ship and the probe.
How many meters below the surface of the ocean will the probe be when it reaches
the ocean floor? Give your answer to the nearest hundred meters.
3.
The map below shows the three tallest mountain peaks in New York State: Mount
Marcy, Algonquin Peak, and Mount Haystack. Mount Haystack, the shortest peak, is
4960 feet tall. Surveyors have determined the horizontal distance between Mount
Haystack and Mount Marcy is 6336 feet and the horizontal distance between Mount
Marcy and Algonquin Peak is 20,493 feet.
The angle of depression from the peak of Mount Marcy to the peak of Mount
Haystack is 3.47 degrees. The angle of elevation from the peak of Algonquin Peak to
the peak of Mount Marcy is 0.64 degrees. What are the heights, to the nearest foot,
of Mount Marcy and Algonquin Peak? Justify your answer.