Heights & Distances Questions and Answers

3 In right triangle ABC mzC 90 CA CB and CB 6 Determine the length of CA in simplest radical form Method Work

Obilique plique cylinder n the right The solids shown have the same height and the same Base area Which has the larger volume they have the same volume it cannot be determined without more information the Right cylinder on the left

Directions After reading each problem identify which method you will use to solve Then use solve the problem Special Ratio HB B Inverse Trig Pythagorean Theorem Trigonometry 3 As shown in the diagram below the angle of elevation from a point on the ground to the top of the tree is 76 If the point is 15ft from the base of the tree what is an equation you could use to determine the height of the tree x Then solve it Method Work 76 15ft a sinx b cos 76 76 15 15 d tan 76 X 15 c tanx 75 seyyadiva x LUO 100 921 Liow way radaadw

1 Identify whether you would use a proportion the Pythagorean Theorem problem below and write it under the image but do NOT solve a An observer on the ground b Adam runs diagonally across a field but Ben runs along the edges How far does Adam run watches a plane above What is the angle of elevation of the plane during the moment pictured below 2000 m 800 m 200 m Adam 120 m Ben C trig or inverse trig for the A 4 m ladder leans against a wall shown below What is the distance between the bottom of the ladder and the wall 4 m 68

1 point Which equation can be used to correctly solve for the value of x in the right triangle cos 49 cos 49 14 X X 14 30 tan 49 4 14 sin 49 X sin 49 4 14 tan 49 144 X 14 8 X 49 14

9 You have a 13 foot long ladder and need to climb to a 12 foot tall roof if you put the top of the ladder at the top of the wall what angle is formed between the ladder and the ground

tion 4 et ered ed out of g ion probability of liking KittKatt given Favorite Candy Bar Kit Kat Children 15 Adults 31 Butterfinge 12 18

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Find the length g correct to two decimal places 39 6 cm

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A radio station obtains a permit to increase the height of their radio tower on Queen Anne Hill by no more than 100 feet You are the head of the Queen Anne Community Group and one of your members asks you to make sure that the radio station does not exceed the limits of the permit After finding a relatively flat area nearby the tower not necessarily the same altitude as the bottom of the tower and standing some unknown distance away from the tower you make three measurements all at the same height above sea level You observe that the top of the old tower makes an angle of 39 above level You move 110 feet away from the original measurement and observe that the old top of the tower now makes an angle of 31 above level Finally after the new construction is complete you observe that the new top of the tower from the same point as the second measurement was made makes an angle of 40 above the horizontal All three measurements are made at the same height above sea level and are in line with the tower Find the height of the addition to the tower to the nearest foot ft

2 A person standing on the level ground is 2 000 feet away from the foot of a 420 foot tall building as shown in the accompanying diagram To the nearest tenth of a degree what is the measure of angle x 2 000 fl 420

at a height of 24 feet If the distance from the bottom of the ramp to the wall is 28 feet determine the 1 The accompanying diagram shows a ramp leaning against a wall where the ramp meets the wall angle x that the ramp forms with the ground X must be shown in order to receive full credit by showing all work and annota

bot shadow a Draw a picture that creates a right triangle to represent the situation b Find all of the angle measures in the triangle Round your answer to the nearest tenth

A guy wire is secured near the top of a television transmitting tower The guy wire meets the ground at an angle of 57 If the height of the tower is 26 ft how long is the guy wire Round to two decimal places as needed

A man is standing 43 ft from the bottom of a flagpole The angle of elevation to the top of the flagpole is 26 How tall is the flag pole Round to two decimal places as needed

Jean and Mildred are standing due east of a 87 m tall tower Jean s angle of elevation to the top of the tower is 19 Mildred s angle of elevation to the top of the tower is 30 How far apart are Jean and Mildred Round to two decimal places as needed

Problem 5 20 Points Find 0 in the figure below 5 5 cm 0 10 cm 5 5 cm

3 In the figure below AABR ABCP and ACAQ are all equilateral triangles Prove that AP BQ CR Hint First show that AABP ARBC A O B C P

h t 4 9t 2 v 0 t h 0 where v 0 is the velocity at which it was launched and h 0 is the initial height in meters

7 Marquise was solving a problem during class Below is the question and his work Solve for the value of x to the nearest thousandth 30 38 tano tan38 0 x 30 tan38 30 x 0 026 There are two errors in his work Circle them in his work and explain how you d change it

x B 4 A C six of 100 Note Figure not drawn to scale magsil In the right triangle above x 60 What is the length of side AB A 7 B 8 C 9 D It cannot be determined from the information given om

34 0 5 y 0 5 3 14 1 2 p q X th The xy plane shows a point of intersection between a line and a parabola The point of intersection has coordinates p q If the vertex of the parabola is at 3 14 what is the value of p

Frequency S 4 2 1 0 1 2 hot 5 7 6 8 3 4 PARTS O Integers 9 10 11 12 The bar graph above shows the distribution of randomly selected integers from 1 to 12 What is the mean of the list of numbers A 5 5 B 6 3 C 7 0 D 10 0

3 If the rope forms a 57 angle with the ground what is the height of the pole to the nearest tenth of a foot Rope 8 ft O 57 Pole

An oil tank has to be drained for maintenance The tank is shaped like a cylinder that is 3 ft long with a diameter of 2 4 ft Suppose oil is drained at a rate of 1 9 ft per minute If the tank starts completely full how many minutes will it take to empty the tank If necessary refer to the list of geometry formulas For your calculations do not round any intermediate steps and use the button on the ALEKS calculator Round your answer to the nearest hundredth minutes X S

A tree on a hillside casts a shadow c 225 ft down the hill Ithe angle of inclination of the hillside is b 26 to the horizontal and the angle of elevation of the sun is a 56 find the height of the tree Round your answer to the nearest foot ft

Find the missing lengths x 10 2 y 10 2 y X 5 6 2 5 6 2 10 6 3 10 6 3 45 x 5 2 y 10 X None of the other answers are correct

Introduction The first Ferris Wheel was built in 1893 for the world s fair in Chicago Illinois Since then engineers have sought to make them larger and stronger Currently the largest Ferris Wheel is the High Roller in Las Vegas Nevada Part 1 A Ferris Wheel is the classic example of a trigonometric function Watch one or all of these videos on The Ferris Wheel

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

a If is in standard position then the reference angle is the acute angle formed by the terminal side of 0 and th Select 3 and that for 8 190 is x axis y axis So the reference angle for 0 110 is b If 0 is any angle the value of a trigonometric function of is the same except possibly for sign as the value of the trigonometric function of 7 So sin 110 sin 190 sin sin and

Kyle converted y 2x 3 to polar form Are his steps correct If not identify the error Step 1 rcos 2 rsin 3 Step 2 rcos0 2rsin 3 Step 3 r cos 2 sin0 3 Step 4 r 3 cos 2sin Select one a Kyle s error occurred in step 4 when he divided by the quantity cos 2sin The fraction can not have the angle in the denominator since it could be zero O b Kyle s error occurred in step 1 where he used the incorrect trig functions for x and y Oc Kyle did not make any errors Od Kyle s error occurred in step 2 where he should have moved the cos to the right side of the equation so the coste would be positive

The table shows the length in inches of fish in a pond 11 18 17 12 3 15 30 19 Determine if the data contains any outliers If so list the outliers O There are no outliers There is an outlier at 3 There is an outlier at 30 There are outlin

15 If px 5 qx 3 8x rx 15 for all values of x and p q 6 what are the two possible values for r A 2 and 4 B 7 and 12 C 22 and 26 D 29 and 39 643 0000

If f x 1 3x 4 for all values of x what is the value of f 4 A 19 B 16 C 13 D 10

A log is seen floating down a river The log is first spotted 45 feet away 7 minutes later the log is 10 feet away making a 60 angle between the two sightings How far did the log travel Round to the nearest tenth

The sun of galaxy X has a diameter of about 736 000 mi with a maximum distance from Planet X s surface of about 49 500 000 mi Planet X s moon has a diameter of 2 648 mi For a total solar eclipse to occur the moon must pass between the sun and Planet X The moon must also be close enough to Planet X for the moon s umbra shadow to reach the surface of Planet X Sun Not to scale The maximum distance that the moon can be from Planet X and still have a total solar eclipse occur is approximately Round to the nearest thousand as needed mi Moon Umbra Planet X

Franklin invests 8 000 in stocks In the first year the stocks decrease in value by 30 Iner the second year however the stocks increase in value by 30 What is the percent change in Franklin s investments over the 2 year period

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Write the equation of a sine or cosine funcatuon yo describe the graph N 2 13 1962 16 15 2 159

distance of 20 feet from a tree the angle of inclination is measured to be 40 degrees Using Trig Gar found the height of the tree to be 22 feet Is this answer reasonable erms of the problem Why or why not

a H b To estimate the height of a mountain two students find the angle of elevation from a point at ground level b 720 meters from the base of the mountain to the top of the mountain is 8 59 The students then walk a 1200 meters straight back and measure the angle of elevation to now be a 37 If we assume that the ground is level use this information to estimate the height of the mountain The height of the mountain is meters

A man standing on the roof of a building 57 0 feet high looks down to the building next door He finds the angle of depression to the roof of that building from the roof of his building to be 34 1 while the angle of depression from the roof of his building to the bottom of the building next door is 63 7 How tall is the building next door Round your answer to the nearest tenth

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Find the value of tan B rounded to the nearest hundredth if necessary B LO 5 D 4 C

What is the volume of this cone Use 3 14 and round your answer to the nearest hundredth 20 in 30 in cubic inches

What is the volume of this triangular pyramid 6 ft 5 ft 10 ft cubic feet

1 Write the side ratios for the following trig functions sine cose tano

ircle A center 12 32 and radius 15 ircle B center 1 4 and radius 10 Which of the following is the necessary transformation translation dilation from A to B to prove that the two circles are similar O Translation 13 units left 28 units down Scale factor reduction ratio 2 3 Translation 13 units left 28 units up Scale factor enlargement ratio 2 3 O Translation 13 units left 28 units down Scale factor reduction ratio 3 2 Translation 13 units right 28 units down Scale factor enlargement ratio 3 2