Heights & Distances Questions and Answers

use the relationship given in the right triangle and the inverse sine cosine and tangent functions to write 0 as a function of x in three different ways It is necessary to rationalize the denominator 1 2 25 6 5

AB is a vertical tower of p units high D and Care in the same horizontal plane as B the foot of the tower The angle of elevation of A from D is x BDC y and DCB 0 The distance between D and C is k units D x Y R k B 6 1 1 Express p in terms of DB and x 6 1 2 Hence prove that p e C ksinetanx sinycose cosysine 6 2 Find BC to the nearest meter if x 51 7 y 62 5 p 80 m and k 95 m 2 5 4 11

8 From the observation deck of a lighthouse 70 meters above sea level the lighthouse keeper can see a fishing boat The angle of elevation from the boat to the lighthouse is 25 What is the horizontal distance to the nearest meter from the base of the lighthouse to the fishing boat A 32 m B 77 m C 150 m D 165 m 70 m 6 Hint the slant height is 9 4 01 Find the surface area of the solid to the right x 25

The points scored on a test for a sample of 40 students are summarized in the following table Number of students Score for each student 7 15 points 14 4 90 80 70 60 Find the mean points scored Round your answer to the nearest tenth

What is the position of D on the number line below Write your answer as a fraction or mixed number th D

The table below summarizes the birth weights to the nearest pound of a sample of 39 newborn babies Number of babies Birth weight of each in pounds 5 3 pounds 10 16 10 6 X 7 Find the mean birth weight of these 39 babies Round your answer to the nearest tenth 8

The spinner below shows 5 equally sized slices Lisa spun the dial 100 times and got the following results Outcome White Grey Black Number of Spins 32 45 23 Fill in the table below Round your answers to the nearest thousandth a From Lisa s results compute the experimental probability of landing on black or grey h Assuming that the spinner is fair compute the theoretical probability of landing on black or

A 13 foot ladder is leaning on a tree The bottom of the ladder on on the ground at a distance of 6 feet from the base of the tree The base of the tree and the ground form a right angle as shown 13 ft 6 ft What is the distance in feet between the ground and the top of the ladder Round your answer to 2 decimal places

Refer to quadrilaterals QRST and FGHJ 13 Name a side that is consecutive with RS 14 Name the side opposite ST 15 Name a pair of consecutive vertices in quadrilateral QRST 16 Name the vertex that is opposite S 17 Name the two diagonals in quadrilateral QRST 18 Name a pair of consecutive angles in quadrilateral QRST 19 Name a diagonal in quadrilateral FGHJ 20 Name a pair of nonconsecutive sides in quadrilateral FGHJ 21 Name the angle opposite ZF R Q S Exercises 13 18 F H G

In the applet below h represents the terminal point s horizontal distance to the right of the circle s center in radius lengths You can vary the value of h by dragging the purple X on the horizontal diameter of the circle The angle s whose terminal point is h radii to the right of the circle s center is are shown 0 30 a Set h to about 0 5 How many radian angle measures 0 between 0 and 7 correspond to this value of h b Set h to about 0 7 How many radian angle measures 0 between 0 and 7 correspond to this value of h c Given any value of h can you determine exactly one corresponding radian measure 0 between 0 and V

CR Geometry B GP 5 Which is the angle of depression from the top of the waterfall to Jim 8 5 6

The given two triangles are similar If the sum of the measures of two angles in a triangle is 85 what is the corresponding sum of the measures of the angles in the other triangle C 85 O 95 O 275 A B

Find the area of the parallelogram 2 5 in 5 2 in 4 8 in

Find the value of h for the parallelogram 27 24 36

One of the standard telephone numbers for directory assistance is 555 1212 How many different permutations of this telephone number are possible

Find the values of x y and z in the figure below Note Input answer as x y z 36

Let y 37 6 be a linear function representing the distance in feet from home for an ant minutes after starting out from a location near its home What does the number 3 represent in this function A The ant is 3 feet from its home after t minutes B The ant started out 3 feet from its home C The ant is crawling at 3 feet per minute D The ant is moving 3 feet every 6 minutes

Graph the function f x 4 2 by moving the key points and the horizontal asymptote as needed Provide your answer below Cr 5 O 1 1 1 T 5

Evaluate the expression under the given conditions sin 0 tan 0 19 12 5 0 in Quadrant III sin p 2 10 10 In Quadrant I

Use the diagram below to answer problems 1 10 P M 1 Name a diameter 2 Name all radii 3 Name all chords 4 Name two tangents 5 Name a secant E 0 6 Name two points of tangency D 7 How many tangents could be drawn containing M and Q Explain your answer 8 How many secants could be drawn containing M and Q Explain your answer

American 12 9 18 21 12 15 Japanese European 8 For a single car chosen at random from the cars on this dealer s lot let A be the event that the car chosen is American and B be the event that the car chosen is compact a For a single car selected from this dealer s lot find P A and P AIB Explain your answers 4 pts b Are A and B independent events Explain 2 pts 12 6 17 IkWhat is the probability that the spinner will land on a green section 1 pt b The spinner is spun and the color is recorded The spinner is then spun a second time and the number is recorded Are these events independent or dependent Explain your answer 2 pts c The spinner is spun and the color is recorded The spinner is then spun a

LISLE Write a rule for the indicated translation from Triangle UVW to U V W U

Let be a Quadrant III angle with cos 0 First assume that 0 values Let s see if this enough information to determine the sign of sin TT 2 sin 3 2 Now assume that 37 0 What interval would 00 sin Next using a half angle identity find the exact value 2 7 V No 3 T 2 0 For this find the exact value 2 OF 7 3 T 4 7 What interval would be in Fill in the following inequality use exact 7 4 OF 1 be in for this Fill in the following inequality use exact values 2 Given your answers above and given that is a Quadrant III angle with cos 0 0 information to determine the sign of sin 2 1 7 1 is this enough

A damsel is in distress and is being held captive in a tower Her knight in shining armor is on the ground below with a ladder When the knight stands 15 feet from the base of the tower and looks up at his precious damsel the angle of elevation to her window is 60 degrees How long does the ladder have to be Show all work

Draw a picture of the angle in standard position labeling x and y axis initial and terminal side a curved arrow with the quadrants labeled Use the Pythagorean Identity to calculate the sine or cosine of the angle 0 Determine if sine and cosine are positive or negative in this quadrant cos 0 2 7 and is between 270 and 360 tan 0 To enter a square root type sqrt To enter x type pi To enter a fraction type Select an answer Select an answer

A 20 meter long cable is used to support a telephone pole holding it perpendicular to the ground If the cable forms a 60 angle with the ground how high up the pole should the cable be attached 10 meters 20 3 meters 20 2 meters 10 3 meters

Listen What is the measure of the indicated missing angle 24 37

Solve for x 6 4x W H U x 4 S Ox 10 Ox 4 Ox 1 Ox 7 R V

A tree with a height of 22 ft casts a shadow 5 ft long on the ground How high is another tree that casts a shadow which is 2 ft long 11 4 ft 8 8 ft 2 5 ft 6 3 ft

Draw the image of this rotation using the interactive graph The direction of a rotation by a positive angle is counter clockwise 9 8 7 6 5 4 3 2 T 9 8 7 6 art 5 Y 4 43 3 2 1 2 3 4 5 6 7 8 x 1 2 3 4 5 6 7 8 9 V

Watch on youtube Suppose a Ferris Wheel has a diameter of 30 meters the center is 19 meters off the ground and it makes 2 revolutions per min Draw this Ferris Wheel labeling the radius height and center Supposing the minimum height of the Ferris Wheel occurs when t 0 write the sinusoidal function for the height as a function of time Lastly graph the function on a coordinate plane do not submit a digital calculator graph label the key points Part 2 Design your own Ferris Wheel determining diameter center and speed Write the function for the height of the Ferris Wheel as a function of time Is your Ferris Wheel realistic Does it travel too fast or too slow

Find the lengths of the missing sides in the triangle Write your answers as integers or as decimals rounded to the nearest tenth 8 X Ox 45 Not drawn to scale Ox 11 3 y 8 Ox 5 7 y 6 9 Ox 8 y 11 3 x 6 9 y 5 7

O False Question 10 1 5 Monological problems are ones for which there are definite correct and incorrect answers and definite procedures for getting those answers True

Sean is hiking the Appalachian Trail from Georgia to Maine The distance of his hike is 2200 miles It took Sean 134 days to complete the hike The data below represent the distance D he had hiked t days after the start of his trip t D t 0 0 19 308 34 578 67 1070 1 Determine the linear regression equation for this data Linear Regression Equation D 3 004t 16 96 57 Round to the nearest tenth as needed In 57 days Sean had hiked 969 724 X miles 91 1715 X 112 1902 2 Interpret the meaning of the slope of this regression model Sean hiked at a rate of approximately 16 96 X miles per day 3 Use your linear regression equation to estimate the total number of miles Sean had hiked in 57 days Round your answer to the nearest mile 134 2200 OF 4 Use your linear regression equation to estimate the total number of days it took for Sean to hike 411 miles Round your answer to the nearest day In 24 days Sean had hiked 411 miles

Type the correct answer in the box Round off your answer to the nearest tenth Jill is standing at the base of her apartment building She measures the angle of elevation to the top of a nearby tower to be 40 Then Jill goes to the roof of her apartment building directly above her previous position and measures the angle of elevation to the top of the same tower to be 30 If the height of the tower is 100 meters the height of Jill s apartment building is meters

QUESTION For which values of a b c and d the following matrix equation is fulfilled 3 20 a 3 2 4 4 C b 6 3 a 3 2 4 4 c a 9 d 2 b 8 7 b REAPUESTAS a Select Select b Select 10 19 11 30 47 54 13 NOTE Choose the N A option in case the other options do not fit the correct answer CH Select

following Write y in terms Initial Value 69 75 153 140 162 96 100 Rate Growth Rate FLVAJ 17 Growth Rate 4 Growth Rate 3 5 Growth Rate 114 Decay Rate 13 Decay Rate 5 Decay Rate 0 1 ite the exponential equation for each of the y y y y y y y Equation 69 1 17 75 1 04 X 153x 1 35 140x 2 14 162 0 87 2 96 0 95 100 0 999 x X X X

O True O False Question 4 1 5 pts Activated ignorance means taking into the mind and actively using information that is false though we mistakenly think it to be true True

Given the horizontal circle readings below answer the following questions 1 FL 99 25 30 2 FL 125 25 25 3 FL 312 47 12 3 FR 132 47 07 2 FR 305 25 18 1 FR 279 25 23 Reduce the horizontal circle readings and enter them in the boxes provided 16 1 2 3 O 11 11

The number of permutations of n different objects is n n n 1 n 2 x x3x2x1 Select one True O False

Assume cos t where t 3 Compute the following cos t cot t sec t

Match the following functions with their equivalent functions cos 0sec csc tan cot Choose Choose sec 1 cos 0 Choose

An airplane pilot over the Pacific sights an atoll at an angle of depression of 5 At this time the hori distance from the airplane to the atoll is 4629 meters What is the height of the plane to the neares Select one a 4647 m b 460 m c 4611 m d 405 m 5 4629 m

Terrance wants to determine the height z of a nearby tree He stands 29 feet from the base of the tree The measure of the angle of elevation from Terrance s feet to the top of the tree is 53 Select all of the following that can be used to find the height of the tree x 29 sin 531 A B C D E F I E 29 sin 37 29 cos 53 29 cos 37 x 29 tan 531 P 29 tan 37 A

13 Examine parallelogram QUAD below D 6x 12 Q B x 11 Select all of the following values that are correct A2 13 cm Q 114 D m U 54 E mZA 126 F m D m D 66 52 1 A U

15 As modeled below a movie is projected onto a large outdoor screen The bottom of the 60 foot tall screen is 12 feet off the ground The projector sits on the ground at a horizontal distance of 75 feet from the screen 60 12 75 0 Determine and state to the nearest tenth of a degree the measure of 8 the projection

6 As modeled below a projector mounted on a ceiling is 3 74 m from a wall where a whiteboard is displayed The vertical distance from the ceiling to the top of the whiteboard is 0 41 m and the height of the whiteboard is 1 17 m 3 74 m 0 41 m 1 17 m Determine and state the projection angle to the nearest tenth of a degree

For problems 1 and 2 find the value of each variable If your answer is not an integer express it in simplest radical form 1 2 12 7 45 b

Nora leans a 24 foot ladder against a wall so that it forms an angle of 76 with the ground How high up the wall does the ladder reach Round your answer to the nearest hundredth of a foot if necessary

A person is standing at the edge of the water and looking out at the ocean see figure The height of the person s eyes above the water is h 1 7 m and the radius of the Earth is R 6 38 x 106 m a How far is it to the horizon In other words what is the distance d from the person s eyes to the horizon Note At the horizon the angle between the line of sight and the radius of the earth is 90 b Express this distance in miles a Number i Units 90 Horizon