Algebra 2 – Probability Review
Name
Algebra 2 – Permutations & Combinations
Permutation –
Combination –
Name
Algebra 2 – Pythagorean Theorem
Name
Pythagorean Theorem
Example:
How high up on the wall will a twenty foot ladder reach if the foot of the ladder is placed five
feet from the wall?
Use the Pythagorean Theorem to find each missing length.
Find the measure of x in each figure.
Solve the following.
1. What is the length of the diagonal of a square whose sides measure 8 cm?
2. The lengths of three sides of a right triangle are consecutive integers. Find them.
3. The lengths of three sides of a right triangle are consecutive even integers. Find them.
4. Find the area of a right triangle with a hypotenuse that measures 17 cm and one leg that
measures 15 cm.
5. The diagonal of a square measures 32 meters. What is the area of the square?
6. The legs of an isosceles triangle measure 6 cm, and the base measures 8 cm. Find the area.
7. A rectangular garden 6 meters wide has a diagonal measuring 10 meters. Find the perimeter
of the garden.
8. How high up on a building will a 15 foot ladder reach if the foot of the ladder is placed five
feet from the building?
9. A baseball infield is a square, each side measuring 90 feet. To the nearest foot, what is the
distance from home plate to second base?
10. A rectangular closet is 2 feet deep, 3 feet wide, and 8 feet high. What is the length to the
nearest inch of the longest pole that can fit within the closet? In other words, find the length
of the diagonal.
11. A flagpole has cracked 9 feet from the ground and has fallen as if hinged. The top of the
flagpole hit the ground 12 feet from the base. How tall was the flagpole before it fell?
12. To find the distance between two points A and B on the opposite ends of a lake, a surveyor
sets a stake at point C so that angle ABC is a right angle. By measuring, she finds AC to be
169 meters and BC to be 65 meters. How far across the lake is point A from point B?
Algebra 2 – Trigonometry
Name
sin a =
cos a =
tan a =
The angle of elevation from a sailboat to the top of a 121 ft lighthouse on the shore measures 16
degrees. To the nearest foot, how far is the sailboat from shore?
Solve the following.
1. A salvage ship is locating wreckage. The ship’s sonar picks up a signal showing wreckage at
an angle of depression measuring 12°. The ocean charts for the region list an average depth
of 40 meters. If a diver is lowered from the salvage ship at this point, how far can the diver
expect to travel along the ocean floor to the wreckage?
2. According to a Chinese legend from the Han dynasty (206 B.C – A.D. 220), General Han Xin
flew a kite over the palace of his enemy to determine the distance between his troops and the
palace. If the general let out 800 meters of string and the kite was flying at a 35° angle of
elevation, approximately how far away was the palace from General Han Xin’s position?
3. Ben is flying a kite directly over his buddy Franklin, who is 125 meters away. His kite string
makes a 39° angle with the level ground. To the nearest meter, how high is the kite?
4. The angle of elevation from a ship to the top of a 42 meter lighthouse on the shore measures
33°. To the nearest meter, how far is the ship from the shore?
5. Meteorologist Wendy Storm is using a sextant to determine the height of a weather ballon.
When she views the weather balloon through her sextant, which is sighted 1 m above the
ground, she measures a 44° angle up from the horizontal. The radio signal from the balloon
tells her that the balloon is 1400 m from her measuring device. To the nearest meter, how
high is the balloon?
6. A lighthouse is observed by a ship’s officer at a 42° angle to the path of the ship. At the next
sighting, the lighthouse is observed at a 90° angle to the path of the ship. This distance the
ship traveled between sightings is 1800 m. To the nearest meter, what is the distance between
the ship and the lighthouse at the second sighting?
7. To calculate the height of a tree, Marie measures the angle of elevation from a point A to be
34°. She measures her distance to be 8 m from the base of the tree. How high is the tree to the
nearest tenth of a meter?
8. A building 14.5 m tall casts a shadow of 11.4 m along the level ground. At what angle do the
rays of the sun hit the ground (to the nearest degree)?
9. A 5.2 m ladder leans against a wall. The bottom of the ladder is 1.9 m from the wall. What
angle does the ladder make with the ground (to the nearest degree)?
10. A kite is 33 m above the ground. The kite string makes an angle of 38° with the ground.
Assuming that the string is taut, how much string is out (to the nearest tenth)?
11. A balloonist records her altitude as 1208 meters. At the same time she measures the angle of
depression of the landing spot to be 17°. How far away, to the nearest meter, is the landing
spot from a point on the ground vertically below the balloon?
12. As it leans against a building, an 8 meter ladder makes an angle of 62° with the ground. How
far is the bottom of the ladder from the base of the building (to the nearest tenth of a meter)?