Heights & Distances Questions and Answers

1 Bob wants to measure the building and decides to use a mirror to do so He stands away from the building and looks into the mirror on the ground moving away or closer to the mirror until he can see the top of the building in the mirror His friend measures the distance between the building and the mirror and the mirror and Bob They draw the following picture to demonstrate the distances Solve for the height of the building 5 ft Cong s by prop of reflections Line of sight 10ft Mirror 100ft h Building Right angle with the ground

Hiption is true for all parallelograms four right angles diagonals bisect each other opposite sides are congruent opposite angles are congruent diagonals intersect at right angles True for all parallelograms Not true

16 Choose the assumption you would make to start an indirect proof Given a b Prove 21 and 22 are not supplementary Fallb G21 and 22 are supplementary H 41 42 JZ1 and 22 are complementary

2 Find the height of the tree www mathwarehouse com 30 43 h

Calculator What is value of x Enter your answer in the box X 4 B 8 X 4 2x 1

YOU DO ROUND 1 Use circle A above where AC 1 inch and m BAD 70 to answer questions x 1 and 2 1 What is the arc length of BC a 1 9 in b 1 2 in 1 0 in d 0 6 in C 1889 D a 1 9 in b 1 2 in c 1 0 in d 0 6 in B 4sh 2 What is the area of sector BAC A

Identify the center and the radius then sketch a graph of the circle Center 3 2 2 190 7 x 3 y 2 4 Radius 4 24

logs Expand each logarithm 1 log 7 2 2log 5 5 log 34 2 85 99 3 log 6 5 11 3 10 7 6 logs 2 2 log 5 11 4 log 3 ab 6 log x y z 8 log 4 10 Jog 106 2

11 4 points Mr Longo and Ms Johnson are celebrating the end of the year by getting ice cream Mr Long ordered 1 scoop of ice cream with a radius of 5 cm and Ms Johnson ordered 2 scoops both with a diame of 6 cm Given that each of their ice cream cones have a volume of 121 cm who has the most ice cream Explain your reasoning

What type of triangle is shown in Clue 15 Classify the triangle by its best name only entering scalene isosceles equilateral or right triangle in the text box starting with a capital letter 8x 1 3x 4

he Height of a Parallelogram What is the perpendicular distance between the line segments AB and CD if the area of parallelogram ABCD is 165 square units 10 b AB 225 VB 0 10 10 6 Q 10 F A 165 AB a D 3 4 C 138 AB 0 9 10 2 9 123 165 15 a units 10

4 If the figure above is rotated continously about g which of the following 3D figures is formed a Cylinder with a diameter of 6 and a height of 2 b Cylinder with a diameter of 4 and a height of 3 c Cylinder with a diameter of 2 and a height of 3 uns biot d Cylinder with a radius of 3 and a height of 2 AU W 2005 baquila F g dw qua tiba

39 36 S 15 cos R cos S sin R sin S tan R tan S 36 39 15 39 15 39 36 39

E B H G Radius Chord Diameter Secant 1111 AB DF GH CD

2 If the measure of LXYZ 70 in C find the measure of ZXCZ X Z C 70 Y

D A 5 X 13 ABCO 51AE 31ED FEF B

Installment Loan Principal Term Length Interest Rate Monthly Payment How much of the first 1500 00 payment for the 4 years installment loan 6 shown in the table will 35 00 go towards principal A 32 90 B 27 50 C 2 10 D 7 50

In this picture B D and F are midpoints AC 50 CE 60 and BD 35 DF

35 5 54 5 OA 7 meters 4 meters OC 3 meters 1 meters The top of a ladder is 10 meters from the ground when the ladder leans against the wall at an angle of 35 5 with respect to the ground If t ladder is moved by x meters toward the wall it makes an angle of 54 5 with the ground and its top is 14 meters above the ground What is xrounded to the nearest meter B 4m D 10 m

A plane takes off at an angle of elevation of 15 and travels in a straight line for 3 000 meters What is the height of the plane above the ground at this instant OA 2898 m OB 2701 m OC 804 m D 776 m

Type the correct answer in each box Round your answers to the nearest tenth A ladder is placed 30 inches from a wall It touches the wall at a height of 50 inches from the ground The angle made by the ladder with the ground is degrees and the length of the ladder is inch

Which of the following best describes the dilation i O i iii only O ii iii only O i ii only O ii iv only ii

Identify the name of the following tool 30

GradeResulls Question 9 O 1 How many lines of symmetry are there in the figure given below O2 Points 1 O 3 0 My Activities Tell me what you

In a laboratory experiment an ultrasound detector located at 8 is used to measure the distances of two moving objects A and C At a certain moment A and C are located as shown in the diagram AB 15 ft BC 14 ft and m ABC 50 What is distance AC B Select one O a length of AC 18 6 ft Ob length of AC 14 5 ft O length of AC 12 3 ft Od length of AC 19 7 ft A 15 ft 28 14 ft C

ven a 6i 4j 4k and b 37 xj 9k find x when a b 2

19 1 point 100 LAND 300 270 10 kr X r r RIVER Find the distance x across the river 30 270 300 27 r

1 point Paige knows that a certain shape is a rectangle She has found the slope of one side to be 2 3 What is the slope of the opposite side What are the slopes of the other two sides opposite side 2 3 other sides 3 2 opposite side 2 3 other sides 3 opposite side 2 3 other sides 2 3 opposite side 3 2 other sides 2 3

10 1 point 60 Solve for x 2 2 2 2 3 1 30

1 A diver jumps from a cliff into the water below The path of the diver is given by the function f x t 4t 12 where f is the height of the diver above water level in metres after t seconds Hassan calculated the following average rates of change in the height of the diver over the following intervals 1 1 1 st 2 AROC 1m s ii 2 st 3 AROC 1m s iii 3 st 4 AROC 3m s Based on these values which of the following statements is FALSE about this situation a The AROC from 3 to 4 seconds is a smaller negative value therefore it implies that the diver is slowing down as it gets closer to the ground b The AROC from 1 to 2 sec is that same as the AROCI for 2 to 3 sec and since the first AROC is positive and the second is negative it implies that a maximum height was reached in the middle at 2 seconds c The diver was at first increasing in height and then decreasing to the AROCS changing from positive values to negative values

4 What inverse trig function can be used to find the measure of angle A tan 1 Cos 1 12 none sin 1

d If 8 2 1 rad then what are your xy coordinates after 2 hours and 6 seconds Round your answers to three decimal places x y Draw an accurate picture of the situation end start end start end start

LPQR is adjacent to LRQS LPQS is 110 and ZRQS is 34 Find the measure of LPQR

Cool Down Lift Off Shortly after takeoff an airplane is climbing 250 feet for every 1 000 feet it travels Estimate the airplane s climb angle while this is happening I B 1000 C 250 A

3 Find all missing 14 0 120 2 Sides and angles using

15 OP is tangent to OT and OS if AB 14 OT 6 and PS 8 Find OP 6 T A B 14 8 S

Campground Map paths tents 1 cm H bathhouse 5 mi What is the actual distance between the two points at the campground O 25 miles O 50 miles O 100 miles O 150 miles 250 miles Scale

The diagram below shows the intersections of several roads Each of the roads is straight The roads First Avenue Ave Second Ave and Third Ave are parallel 300 1236 06 3 Fint 406 m Marisa drives from point A to point B along Broad St and then from point B to point C along Third Ave What distance to the nearest meter did she drive

A 15 foot conveyor belt for raising and lowering supplies is leaning against a building at a 30 angle with the ground as shown Select one 15 feet Which trigonometric equation could be used to find x the distance in feet from the base of the conveyor belt to the building O 30 x 15 sin 30 x 15 cos 30 Xx sin 30 15 15 Cos 30

Round your answer to the nearest hundredth What is the height in feet of the tree The height is feet 42 31 20 ft

15 Find the EXACT area and perimeter A A 6 in 45 B 12 in Boti 6

7 21 53 X round it n CO X too 10 st

8 A building with 12 f1 Cover ramp The i ramp horizontal distance being makes installed an the ground Find the that the at a angle of 110 height and camp will

Consider the right triangle shown below that has an interior angle measure of radians ii What is the value of cos 0 Preview COF A mode 0 00 a Use the slider in the applet above to show a circle centered at the left most vertex of the triangle b Consider the terminal point P i What is the measure of the terminal point s vertical distance above the center of the circle in units of the radius of the circle Preview ii What is the value of sin 0 sin 0 c Consider the terminal point P i What is the measure of the terminal point s horizontal distance to the right of the center of the circle in units of the radius of the circle 2 4 cm Preview 8 2 06 cm Drettien 1 23 cm

3 Determine the volume of the figure below Round to the nearest tenth 1

Question 5 Find the missing angles and sides of the following two congruent triangles B 13 60 A Points 2 13 C Q P R O All angles 60 and All sides 13 units Angle B Angle C Angle P Angle R 45 Angle Q 60 side AC PR 16 side PQ PR 13 Angle B Angle C Angle P Angle R 65 Angle Q 60 side AC PR 16 side PQ PR 13 Angle B Angle C Angle P Angle R 60 Angle Q 60 side AC PR 16 side PQ PR 13 Rese Rese afte asse Q

Question 10 Points 1 If the point A 10 4 is reflected above the line y x Identify the transformed point O A 4 10 O A 4 10 O A 10 4 O A 10 4

19 Determine distance X T X 3 05cm 55 05 11 c 5 00 cr

Find the surface area of the square pyramid 8 m OA 192 m2 OB 448 m OC 256 m OD 384 m2

Draw a plane intersecting a cube to get the cross section indicated rectangle OA OB C OD