Geometry Questions

A 25 foot ladder leans against a wall so that it is 20 feet high at the top The ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up How much higher is the top of the ladder now Hint L t 15 2x be the distance from the base of the ladder to the wall 2x Save Exit The top of the ladder is feet higher now L

An 80 foot rope from the top of a tree house to the ground forms a 45 angle of elevation from the ground How high is the top of the tree house Round your answer to the nearest tenth of a foot feet

Find the value of b Round your answer to the nearest tenth B 40 10 12 A

Find the area of AABC with side lengths b 9 and c 14 and included angle A 145 Round your answer to the nearest tenth The area of the triangle is about square units

24 6 27 Which of the following trigonometric ratios are correct 20 b X cos 20 cos 20 sin 20 Otan 20 Osin 20 a 1 X tan 20 b X X X b a X X b a

Write sin 49 in terms of cosine sin 49 COS O

Classify a triangle with each set of side lengths as acute right Acute or obtuse Right Obtuse

Find the exact value of x X 10 X 6

6 AB is tangent to circles P and Q below If AP 5 AZ x 4 BZ x and BQ 3 Determine the length of PZ in simplest radical form 5 N B

1 AE is tangent to circles D and C If EB x 8 DE 8 AB 6 and AC x a Find DB in simplest radical form b Find the length CB E B

5 In the diagram above AC and AD are tangent to circle B at points C and D respectively If CB 4 and AE 8 determine the length of AC in simplest radical form A E B

4 In the figure d e and fare parallel lines What is the value of x x 20 70

3 8 04 Review A right triangle has one leg that double the length of the other If the hypotenuse is 5 what is the length of each leg

3 In the figure c d What are the measures of 21 and 22 1 2 4 3 5 75 8 7

4 SAT Question Equivalent Expressions Which of the following is equivalent to 3x4 3 a 3 x 1 b 3 x 1 c 3 x 1 x 1 d 3 x 1 x 1 x 1

2 In the accompanying diagram BA is tangent to circle O at A Radii OA and OC are drawn and OC is 2 determine and state the length of AB extended to intersect at BA at B If AO 3 and BC C B

Find the perimeter and area of the figure The perimeter is 66 ft Simplify your answer Type an integer or a decimal The area is Simplify your answer Tyne an integer or a decimal 16 ft 1 1 5 ft 12 ft 12 ft

17 Find the geometric mean of 6 and 48 Solve for x 18 20 24 x 18 20 30 30 X Solut 19 21 3 200 18 24 X V 15 late 17 18 19 20 21 stoc brif barutosta gofapt lonke l euapomn nosta

Determine whether the triangle with the given side lengths is acute right obtuse or not a triangle 8 3 9 10 9 6 12 19 10 21 28 35 Not a A Acute Right Obtuse Not a A Acute Right Obtuse Not a A Acute Right Obtuse Gina Wilson All Things Algebra LLC 2014 2018

Which solid figure is represented by this globe x x X A cylinder B cube C C cone sphere

Solve for x 1 19 3 30 33 X 16 2 4 X 16 5 22 9 2 25 16 1 2 3 4 5 6 7

Organizers of an outdoor concert will use 320 feet of fencing to fence off a rectangular VIP section What is the maximum area that they can fence off 4x X A 6 400 square feet B C 12 800 square feet E 25 600 square feet D 24 000 square feet 3 200 square feet

During strenuous work a human body generates about 2 400 BTUs of body heat per hour If 6 football players are in a gym that is 12 ft x 18 ft 10 ft lifting weights how many BTUs per cubic foot do they produce in 2 hours to the nearest tenth A B C 133 3 BTUs ft3 13 3 BTUs ft3 66 7 BTUs ft3

A rectangular corn field yielded 2 200 000 ears of corn The dimensions of the corn field are 800 yards by 550 yards How many ears of corn per square yard did the corn field yield x x A 25 per square yard B C 10 per square yard 5 per square yard D 50 per square yard

Which solid figure is represented by this soup can x A cone B rectangular prism C cube D cylinder Mer ar Roth Thank Me QUALITY

x Po has a frame that is 9 in x 8 in What is the maximum area the picture can have to fit in the frame A 72 sq in B 81 sq in C 63 sq in D 9 in 96 sq in 8 in

Which solid figure is represented by this globe X 1x A cylinder B cube C cone D sphere G G G

To indirectly measure the distance across a lake Lauren makes use of a couple landmarks at points L and M She measures KO OM and NO as marked Find the distance across the lake LM rounding your answer to the nearest hundredth of a meter M L 95 m Diagram is not to scale 109 5 m 125 m K HANDM

Express your answer to the nearest tenth of a foot Enter your answer in the box 42 8 Part D A In the future Luke has plans to construct a circular storage bin centered at coordinates 50 40 on the plan Which of the listed measurements could be the diameter of a bin that will fit on the plot and be at least 2 feet away from the warehouse Select all that apply 10 feet B D 15 feet 18 feet 22 feet feet 25 feet U139 30 20 0 UT 11 20 2 U121 400 U521 and or 42 8

4 A manufacturer is designing a new container for their chocolate covered almonds Their original container was a cylinder with a height of 18 cm and a diameter of 14 cm The new container can be modeled by a rectangular prism with a square base and will contain the same amount of chocolate covered almonds Chocolate Covered Almonds 14 cm If the new container s height is 16 cm determine and state to the nearest tenth of a centimeter the side length of the new container if both containers contain the same amount of almonds 18 cm Chocolate Covered Almonds A store owner who sells the chocolate covered almonds displays them on a shelf whose dimensions are 80 cm long and 60 cm wide The shelf can only hold one layer of new containers when each new container sits on its square base Determine and state the maximum number of new containers the store owner can fit on the shelf

2 The town of Manchester population 50 000 has the shape of a rectangle that is 5 miles wide and 7 miles long Part A What is the population density in people per square mile in Manchester Round your answer to the nearest whole number of people per square mile Part B The town of Manchester contains a business area in the center of town that has the shape of a disk with a radius of 1 mile If no one resides in the business area what is the population density in Manchester in people per square mile outside of the business area Round your answer to the nearest whole number of people per square mile

5 A scale drawing of Corinne s bedroom floor is shown below All given dimensions are in feet All intersecting line segments shown are perpendicular Corrine wants to completely cover the floor with square hardwood tiles Each tile has a side length of 1 foot and no tiles will be cut How many tiles will Corinne need to cover the floor 5 69 63 C 79 84 11 6 9

1 The density of a certain type of paint is 1 2 grams per cubic centimeter A garage door that is 3 meters tall and 7 meters wide is to be painted with a 1 millimeter thick coat of paint on the outside only What is the mass in kilograms of the paint that will be needed to paint the door kg

3 A shipping container is in the shape of a right rectangular prism with a length of 12 feet a width of 8 5 feet and a height of 4 feet The container is completely filled with contents that weigh on average 0 25 pound per cubic foot What is the weight in pounds of the contents in the container A 92 B 408 c 102 D 1 632

Question 5 1 point L K P M N If mON 21 degrees and m LPM 44 degrees Fine mLM

G H If m GHI 87 degrees what is the measure of ZJ Your Answer

F point Your Answer E G D If E 33 and D is 63 what is the measure of arc FED

Question 10 1 point N Your Answer M If LM 6 and KL 9 find the length of MN Roun your answer to one decimal place

Question 6 1 point E H G Given mGH 21 degrees and mEF 98 Find mZJ

Question 8 1 point B Your Answer E C If BE 10 ED 12 and EC 4 what is the lengt of AE

at fand g are inverse functions a algebraically and b graphically 7x 1 3 4x g x 3 7 g x 3 x 4

24 A gram 4 B is tange 25 B 12 8 26 B C 15 9 A

LL F E G Your Answer D If E 33 and D is 63 what is the measure of arc FED

W 1 point Retake question Y X If mVX 10 find m Y

M N P MQN is 12 and arc OP is 137 What is the measure of arc MPO Your Answer

Jestion 1 point Retake question K P If mON 23 degrees and m LPM 45 degrees Find mLM Your Answer

S R Your Answer Q Not drawn to scale If PQ 9 and OP 8 QR 8 find the length of SR Round your answer to one decimal place Sign out Fel

A Question 10 1 point Retake question K N Your Answer M If LM 4 and KL 14 find the length of MN Round your answer to one decimal place

17 Sil O A OB O C C 53413 16 20 B 12

A B C From ZC side AB is the opposite adjacent hypotenuse