Geometry Questions

A boy who is 5 feet 6 inches tall casts a shadow that is 8 feet and 3 inches long What is the measure of the angle of elevation of the sun A as shown in the picture Round to the nearest degree Be careful with your units in this problem

How far from the base of a building must the bottom of a 15 foot ladder sit for it to make a 52 angle with the ground Round to the nearest tenth of a foot 15 ft bo

5 A person sights a boat from 235 feet above sea level as shown If the angle of depression from the man to the boat is 21 then determine the boat s distance to the edge of the cliff to the nearest ten feet 235 ft 21

A long wire is attached to the top of a 175 foot tall electrical transmission tower If the wire needs an angle of 65 with the ground then how long must it be Round your answer to the nearest foot feet 65 make 175 feet person sights a boat from 235 feet above sea level as shown If the angle of depression from the man to boat is 21 then determine the boat s distance to the edge of the cliff to the nearest ten feet

Verify the identity Simplify at each step 9 cos x 9 sin x 9 cos 2x x 9 cos x 9 sin x 9 cos x sin x 9 cast 1 sin x

Consider the angle shown below whose vertex is at 2 2 5 A circle with a radius 1 7 units long is centered at the vertex of the angle and the terminal point at 3 4 3 46 9 Preview 4 3 4 3 46 F 2 2 5 3 2 Y a The terminal point is how many units to the right of the center of the circle units Preview b The terminal point is how many radit to the right of the center of the circle radi Preview c Therefore the radian measure of the angle is 3 5 I

gra Hint Graph the vectors on graph paper then draw the resultant vector Select one a b Vectors choose the image which best represents the difference of u v

Given a 61 43 4k and b 3i xj 9k find x when a b 2

The figure below shows quadrilateral ABCD and a line of reflection A B C R 9 x y 8 7 6 5 4 3 2 B x y C 4 5 6 7 Determine the coordinates of A B C and D using only reasoning that is without folding x y 1 2 3 D 1000 00 8 T 9

Given the vector 6 12 6 12 1 with a directional angle of

17 Solve for the surface area and volume of the composite figure made of a right cone and hemisphere half sphere 15 points 10 in 13 in

Given a vector begins at 3 and ends at 2 1 then the components of the vector are 4

formation is given about AABC Determine if the information gives one triangle two triangles or no triangle Solve the resulting triangle s Round the ngths of sides and measures of the angles to 1 decimal place if necessary c 12 b 5 B 38 There is no triangle that can be formed from the given information O There is one unique triangle that can be formed from the given information A a O There are two triangles that can be formed from the given information Triangle 1 S E

Solve the triangle For the sides give an expression for the exact value of the length in terms of sine and approximate to I decimal place Part 1 of 3 A B 64 Part 1 3 Part 2 of 3 Skin Part Check b 71 118 6 sin cos 97 4 a 00 B Save For Show Transcribed Text

Given the information a vector has length 8 with South direction it would be drawn from the the point 0 6 the origin anypoint and extend

i 8j 4w 6i 3j 3w I i 7 6 5 4 3 W

0 This is a vector wit 2 03 magnitude direction

each circle 2 2 1 x 1 y 3 2 2 3 x 1 y 4 2 x 2 y 1 16 2 4 x y 3 25 4 9

6 x 1 y 3 4 y 6 5 4 3 2 1 6 5 4 3 2 1 11 2 31 0 45 6 6 5 4 3 2 1 4 7 x 2 y 1 16 y 6 5 4 3 2 1 6 5 4 3 21 1 0 11 2 3 4 5 6 8 x 1 y 4 9 y 6 5 4 3 2 1 0 N F1 2 6 5 4 3 2 1 31 4 5 6 6 5 4 3 2 1 1 2 3 4 5 6 9 x y 3 25 ya 0 1 2 3 4 5 6 1 1 2 3 4 5 6 X A 1 2 3 4 5 6 X

2 Diameter of 12 3 Diameter of 22 For problems 4 10 write the equation of the given circle 4 Center 12 7 Radius 4 5 Center 2 14 Radius 5 6 Center 12 10 Radius 7 7 Center 6 4 Radius 8 8 Center 3 13 Diameter 2 9 Center 1 3 Diameter 8

problems 8 10 Leave your answers in terms of pi 240 14 in 315 19 12 16 ft 12 ft

with a diameter of 14 inches 3 A sector that is two thirds the area of a circle with a radius of 10 yards For problems 4 7 find the area of each sector Write your answer as a decimal rounded to the nearest tenth 4 5 6 60 10 in 3 m 150 3x 4 cm

Find the value of the variable 24 A X D B Answer T 40 13 Find the value of the variable S C

the standard equation of the circle in the graph Center 4 0 4 5 et one a x 4 2 y2 25 0 x y 25 C x 4 2 y2 25 d x y 16 e the standard equation of the circle in the graph 2 1 4 1

of the following statements is false one Every chord is part of a secant Every diameter is part of a secant Every diameter is a chord Every chord is a diameter the standard equation of the circle in the graph one 012 o 212 19

Which is the equation of a circle with center 2 3 and radius r 5 Select one O a x 2 2 y 3 25 b x 2 2 y 3 25 c x 2 y 3 10 d x 2 2 y 3 10 Which is the equation of a circle with diameter AB where A 5 4 and B 1 4 Select one a x 5 2 y 4 10 b x 5 y 4 100 c x 2 2 y2 25 d x 2 y 5

arc Leave your answers in terms of pi 8 9 315 150 3r 8 cm 19 ft 13 ft

2 Find the distance around one fifth of a circle with diameter of 14 inches 3 Find the distance around five sixths of a circle with diameter of 20 yards For problems 4 7 find the length of the darkened arc Round your answers to the nearest tenth 4 5 6 11 ft 315 270 3x 13 ft 16 ft

the figure below what is m C D B elect one a 50 b 15 c 35 30 d 65 N d 7 5 the figure below what is the value of z 4 elect one a 2 9 Ob 8 75 c 5 6 E 100

Which of the following is the graph of x 2 2 y 1 9 elect one a b C d Lify FRE 2 O

What is the equation of the circle with center 0 0 that passes through the point 8 3 Select one a x y 73 b x y 55 c x 8 2 y 3 55 d x 3 y 3 73 Check

degrees the measure of arc FH is 138 degrees and the measure of arc HB is 20 degrees Find the measure of FPD 3 points P B E 9 In the diagram below the measure of arc SQ is 106 degrees and the measure of arc PR is 120 degrees Find the value of x 3 points

X 6 X 4 12 12 Find the value of x 3 points S x 5 N x 8 M K 4

he center and radius of a circle with equation x 3 2 y 6 4 one center 6 3 r 2 center 3 6 r 4 center 3 6 r 4 center 3 6 r 2 ck is the equation of a circle with center 3 5 that passes though the point 4 10 tone x 3 2 y 5 2 74 x 4 y 10 74 x 3 2 y 5 226 x 4 y 10 226

2 The equation x 6x y 6y 9 0 is an equation of a circle in expanded form Complete the square to find the center and radius and then write the equation of the circle in standard form To earn full credit you must show your work a center b radius c Equation

ow wattage radio station can be heard only within a certain distance from the station On the graph ow the circular region represents that part of the city where the station can be heard and the cen e circle represents the location of the station Which equation represents the boundary for the regic ere the station can be heard ep elect one 4 4 O a x 6 2 y 1 32 b x 6 y 1 32 c x 6 2 y 1 16 Od x 6 2 y 1 16 X

Vrite an equation of a circle with diameter AB where A 3 0 and B 7 6 Answer Vo 0 TU a

e the standard equation for a circle er 10 6 r 6 ct one a x 6 y 10 36 b x 10 y 6 6 c x 10 2 y 6 6 d x 10 2 y 6 36 heck ite the standard equation for a circle ter 6 8 that passes through 0 0 lect one a x 6 2 y 8 196 b x 6 2 y 8 14 c x 6 2 y 8 100 Od x 6 2 y 8 10

y x 4 Graph y x 4 Choose the correct graph below G OB OA 2 2 OC 2 2 OE 3 5 OG The graphs do not intersect oo Determine any points of intersection Choose the correct answer below O C OB 5 3 O D 2 2 and 2 2 OF 5 3 and 3 5 D

The equation of a sphere is similar to the equation of a circle The equation of a sphere with center h j k and radius r is x h y j z k r M 2 3 3 is the center of a sphere passing through T 0 4 2 What is the radius of the sphere What is the equation of the sphere The radius of the sphere is Type exact answers using radicals as needed

Write an equation of a circle with diameter AB A 6 6 B 14 14 Choose the correct answer below OA x 10 y 10 6 OC x 10 y 10 32 O E x 10 y 10 32 OG x 14 y 14 6 OB x 10 y 10 14 OD x 6 y 6 14 OF x 10 y 10 32 OH x 10 y 10 32

Sketch the graphs of each equation Find all points of intersection of the pair of graphs x y 8 y x 4 Graph x y 8 Choose the correct graph below OA OB 15 O C G O D

1 point Consider the triangle below not drawn to scale b C C 11 01 ZA 16 14 ZB 33 768429 a Let a 4 b 8 and ZC 130 Find the length of side c and measure of the angles ZA and ZB in degrees Give your answer to at least 3 d places

What values are required for A and B so that 3pi 4 is a solution to the following question Asin x Bcos 2x 1 A R

QUESTION 17 1 POINT The polynomial f x given below f x x 3 7x 2 24x 32 Find the other has 1 as a zero zeros of f x List the zeros separated by a comma

a building The height of the ros by h t 8t 2 80t 25

e line parallel to g x 6x 8 and passing through the point 4 2 Write the form

Glven Two Points Write the equation of the line with the two given points 5 1 3 and 3 5 6 1 4 and 6 1

Select the simplification that accurately explains the following statement oot 4 2 2 1 4

What is the value of sec 0 if the terminal side of angle 0 intersects the unit circle in the first quadrant at x