Geometry: Chapter 8 Review: Right Triangles and Trigonometry
If your last step of a problem is tan(x)=0.902, how do you solve for x, the angle? (2 ways)
1. look for that decimal in the chart 2. on a calculator, tan^-1(0.902) and the answer will the the angle measure (some calculators you may have to use the shift button)
66
A 20ft ladder leans against a wall so that its base is 8 ft from the base of the wall. What is the angle of elevation of the ladder, to the nearest degree?
56
A boat is 100 meters from the base of a 150 meter tall cliff. To the nearest degree, what is the angle of depression from the top of the cliff to the boat?
64
A boat is 120 meters from the base of a 250 meter cliff. What is the angle of depression, to the nearest degree, from the top of the cliff to the boat?
35
A man at ground level measures the angle of elevation to the top of the building to be 67°. If at this point, he is 15 feet away from the building, what is the height of the building, to the nearest foot?
67 ft
A person's eye level 6 feet from the ground sights the top of the building at 49 degrees while standing 53 feet away, how tall is the building?
<LKM
Carlos is making some observations from the roof of a building. Which angle is the angle of elevation from Carlos to the helicopter?
CAH
Cos = adjacent/hypotenuse
37°
Determine the angle.
74°
Determine the angle.
14.438
Determine the side length. Round to the thousandths.
8.756
Determine the side length. Round to the thousandths.
9.563
Determine the side length. Round to the thousandths.
4√5
Find the geometric mean between 10 and 8.
2√11
Find the geometric mean between 2 and 22.
20
Find the geometric mean between 25 and 16.
9
Find the geometric mean between 3 and 27.
2√3
Find the geometric mean between 3 and 4.
12
Find the geometric mean between 36 and 4.
2√7
Find the geometric mean between 4 and 7.
10
Find the geometric mean between 5 and 20.
2√10
Find the geometric mean between 8 and 5.
18
Find the geometric mean between 81 and 4.
5013
From a boat on the river below a dam, the angle of elevation to the top of the dam is 24°. If the dam is 2039 feet above the level of the river, how far is the boat from the top of the dam (to the nearest foot)?
16
From a point on the ground 12 ft from the base of a flagpole, the angle of elevation of the top of the pole measures 53°. To the nearest foot, how tall is the flagpole?
2556
From an airplane at an altitude of 1200 m, the angle of depression to the base of a building on the ground measures 28°. Find the distance, to the nearest meter, from the plane to the building.
28.6feet
A 12-foot tree casts a 22-foot shadow. Find the angle of elevation from the tip of the shadow to the top of the tree. Round the answer to the nearest tenth.
6.2ft
A 20-ft ladder is placed against a wall at an angle of 72 degrees with the ground. How far from the base of the wall is the bottom of the ladder?
4846.609 ft
A ranger is at the top of a 254-ft lookout tower located on a flat plain. She spots a fire at an angle of depression of 3° from the top of her tower. How far away is the fire from the base of the tower? Remember the units!
188
A salvage ship's sonar locates wreckage at a 12° angle of depression. A diver is lowered straight down 40 meters to the ocean floor. To the nearest meter, how far does the diver need to walk along the ocean floor to the wreckage?
1967
A skier is at the top of a mountain. He estimates the angle of depression from where he is now to the flag at the bottom of the course to be 24°. He knows he is currently at an altitude of 800m. To the nearest foot, how long is the path he will ski?
69
An airplane is 900 ft horizontally from an airport and 2500 ft from the airport. To the nearest degree, find the angle of elevation from the airport to the airplane.
11
An airplane rises vertically 1000 ft over a horizontal distance of 5280 ft. What is the angle of elevation the plane makes from the ground, to the nearest degree?
60
An observer is 100 feet from the top of a cliff and 50 feet from the base of the cliff. Find the angle of elevation from the observer to the top of the cliff., to the nearest degree.
282
An observer standing on top of a vertical cliff spots a nest in the adjacent valley at an angle of depression of 12°. The cliff is 60m tall. To the nearest meter, how far is the nest from the base of the cliff?
49.2 ft
At a point 153 feet from the base of a building the angle of elevation to the top of the building is 56 degrees. From the same point the angle of elevation to the top of the flagpole on top of the building is 61 degrees, how tall is the flagpole?
101
Benny is flying a kite directly over his friend Frank who is 125 meters away horizontally. When he holds the kite string down to the ground, the string makes a 39° angle with the ground. How high is Benny's kite, to the nearest meter?
24
Buildings A and B are across the street from each other, 35m apart. From a point on the roof of Building A, the angle of depression to the base of Building B is 34°. To the nearest meter, how tall is Building A?
77
From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of depression of 40º. If the distance from the ranger to his partner is 100 ft, how far is the ranger's partner from the base of the tower (to the nearest foot)?
33.9 ft
If a person sights the top of a tree at an angle of elevation of 37 degrees and sights the base of the tree at an angle of depression of 17 degrees while standing 32 feet from the tree, how tall is the tree?
80 degrees
If a tower 37 meters high casts a shadow 6.2 meters long, what is the angle of elevation of the sun to the nearest degree?
60.4feet
Kendra is flying a kite 35 feet in the air. The angle of depression from the kite to where Kendra holds the string is 32. If Kendra holds the string 3 feet off the ground, what is the distance from her hands to the kite? Round your answer to the nearest tenth.
What is the phrase to remember the trig functions?
SOH CAH TOA
SOH
Sin = opposite/hypotenuse
12
Solve for x.
15
Solve for x.
48
Solve for x.
6
Solve for x.
60
Solve for x.
2√13
Solve for y.
TOA
Tan = opposite/adjacent
Angle of Depression
The angle created by looking down from your horizontal eye sight
Angle of Elevation
The angle created by looking up from your horizontal eye sight
Angle of Elevation
The angle formed by a horizontal line and an observer's line of sight to an object above the horizontal line
Angle of Depression
The angle formed by a horizontal line and an observers line of sight to an object below the horizontal line
422
The angle of elevation from a sailboat to the top of a 121-ft lighthouse on the shore measures 16°. To the nearest foot, how far is the sailboat from the shore?
64.674 m
The angle of elevation from a ship to the top of a 42-m lighthouse is 33 degrees. How far is the ship from the lighthouse? Round to the thousandths.
88
The angle of elevation from a ship to the top of a 48-meter lighthouse on the shore measures 33°. How far is the ship from the top of the lighthouse, to the nearest meter?
59
The distance from a point on the ground to the top of the flagpole is 44 feet. The point is 26 feet from the base of the flagpole. Find the angle of depression from the top of the flagpole to the point on the ground, rounded to the nearest degree.
Hypotenuse side
The side that is across from the right angle
Opposite side
The side that is farthest away from the circled angle
Adjacent side
The side that is next to the circled angle, but not the hypotenuse
What is the relationship between the angle of elevation and angle of depression?
They are congruent!
2003
What year did Mrs. Mazza start working at Shore?
40/41
Write the ratio: Cos Z.
4/5
Write the ratio: Sin A.
8/15
Write the ratio: Tan Z.
3348
You are skiing on a mountain with an altitude of 1200 meters. The angle of depression to the bottom is 21°. To the nearest meter, how far do you ski down the mountain?
17
You are standing 22 feet away from a tree, and you measure the angle of elevation from the ground to the top to be 38°. How tall is the tree, to the nearest foot?
13
You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26°. To the nearest foot, what is the length of the base of the ramp?
For what triangles is SOH CAH TOA used?
only RIGHT triangles
