Heights & Distances Questions and Answers

Five students Adriana Ben Chandra Diana and Ernesto would each like one of the four spots at the regional science fair Their names are placed in a hat and four names a chosen at random to decide who attends the fair What is the theoretical probability that Chandra will be chosen as one of the science fair participants 25 60 75 OOC

A state trooper is hidden 30 feet from a highway One second after a truck passes the angle 8 between the highway and the line of observation from the patrol car to the truck is measured See the illustration Complete parts a c a If the angle measures 17 how fast is the truck traveling Express the answer in feet per second and in miles per hour If the angle measures 17 the speed of the truck is feet per second Do not round until the final answer Then round to two decimal places as needed

A radio tower is located 325 feet from a building From a window in the building a person determines that the angle of elevation to the top of the tower is 38 and that the angle of depression to the bottom of the tower is 28 How tall is the tower Round answer to one decimal place feet

Find the value of x Round to the nearest tenth 1 3 5 60 m 40 22 18 900 ft 12 000 ft XXXXXX 4 6 X 1 000 ft 8 Two office buildings are 100 ft apart as shown From the edge of the roof of the shorter building the angle of elevation to the top of the taller building is 28 and the angle of depression to the bottom is 42 How tall is each building Round to the nearest foot 48 80 ft 7 Rachel is attempting to find the area of the triangle shown She remembers the formula A bh What line should she draw to apply the formula What is b What is h What is the area Round to the nearest tenth 2 800 ft 6 cm 28 70 100 ft 33 9 cm

nd the exact value of each of the remaining trigonometric functions of 0 tan 0 15 8 and sin 0 0

Determine the directrix of the conic with polar form r 6 3 cose

Test the claim about the difference between two population means and 2 at the level of significance a Assume the samples are random and independent and the populations are normally distributed Claim 0 01 Population statistics 3 2 0 1 7 Sample statistics x 14 n 30 X 16 n 27 Ha H1 H Determine the standardized test statistic Z Round to two decimal places as needed Determine the P value P value Round to four decimal places as needed What is the proper decision OA Fail to reject Ho There is enough evidence at the 1 level of significance to reject the claim OB Reject Ho There is not enough evidence at the 1 level of significance to reject the claim OC Reject Ho There is enough evidence at the 1 level of significance to reject the claim OD Fail to reject Ho There is not enough evidence at the 1 level of significance to reject the claim

5 5 ft 74 10 ft feet zearn Richland School Di Find the height of the top of the goal post rounded to the nearest tenth of a foot

To calculate the cost of painting his silo a farmer must find its height The farmer uses a cardboard square to line up the top and bottom of the silo as shown in the diagram below Approximate the height of the silo DR

In order to meet ADA Americans with Disabilities Act requirements a wheelchair ramp must have an angle of elevation of no more than 4 8 A builder needs to install a ramp to reach a door that is 2 5 feet off the ground 11 Is 20 feet long enough for the straight line distance of the ramp to meet the requirements What angle of elevation will this ramp have A 20 foot ramp will have an angle of elevation of approximately

A roof has a cross section that is a right triangle The diagram shows the approximate dimensions of this cross section Find the height h of the roof Round your answer to the nearest tenth 20 ft The height of the roof is about 23 9 ft feet h 13 ft

You are holding a kite string in your hand The angle of elevation from your hand to the kite is 53 and the distance to the kite is 300 feet Your hand is 4 feet above the ground How high is the kite Round your answer to the nearest tenth of a foot feet

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

An observer D is located 500 feet from a school i The observer notices a bed gaa school You must show all work and calculations to receve tu creat 39 500 feet

10 G Two triangles are shown D L 3 N T2 8 7 6 5 2 0 2 3 4 E7 8 5 6 y 6 8x Which sequence of transformations could be performed on AEFG to show that it is similar to AJKL A Rotate AEFG 90 clockwise about the origin and then dilate it by a scale factor of with a center of dilation at the origin 1 2 B Rotate AEFG 90 clockwise about the origin and then dilate it by a scale factor of 2 with a center of dilation at the origin 1 2 C Translate AEFG 1 unit up then reflect it across the x axis and then dilate it by a scale factor of with a center of dilation at the orig Reflect AEFG across the x axis then reflect it across the line y x and then dilate it by a scale factor of 2 with a center of dilation the origin

hemisphere and a cylinder on a cylindrical base The dimensions are shown below The base is slightly wider than the globe with a diameter of 8cm and height of 1 8cm 3cm 2cm 1cm H Part A Find the volume of water in the snow globe Part B A package of silicon snowflakes containing approximately 500 snowflakes is put into the globe When the globe is shaken up what is the population density of the snowflakes in the water Part C If each globe is individually packaged into a box what are the minimum dimensions of the box Part D The globes are ordered by the retail store in cases of 24 Design a rectangular case to hold 24 globes packaged in individual boxes What is the minimum dimensions and volume of your case

A bag contains 2 red 5 blue and 3 green balls A ball is chosen at random The probability of choosing a read ball is 15 What is the probability of not choosing a red ball

You choose a card at random from a standard deck of cards The probability of drawing a red king is 1 26 What is the probability of not drawing a red king

For each scenario below choose the best graph a A plane goes slower after landing Plane s Speed Time Bird s Distance from Nest Plane s Speed Time b A bird flies away from its nest to go hunting O Bird s Distance from Nest Time Time Plane s Speed Bird s Distance from Nest y Time Time

A car of mass 750kg has a maximum power of 30kW and moves against a constant resistance to motion of 800N Find the maximum speed of the car a on the level b up an incline of arcsin 1 10 to the horizontal c down the same incline

AABC has sides AB 7 BC 6 AC 9 CD and CE are interior and exterior angle bisectors of AABC Find DE

14 5 and w 2 ur answer in exact form v W

1 point Attempt 1 of Unlimited 7 our answer in exact form if nece

4 A pilot wants to fly on a bearing of 67 3 By flying due east he finds that a 51 mph wind blowing from the south puts him on course Find the airspeed of the plane Find the ground speed of the plane

e on a hillside casts a shadow c 235 ft down the hill If the angle of inclination of the hillside is b 20 to the horizontal and the angle of elevation of the sun is a 50 find the height of the tree Round your answer to the nearest foot ft

Use properties of logarithms to evaluate log4 6400 log4 100 A 2 41 B 6 31 1 81 D 3

Achilles is piloting a 65 meter tall giant death robot looking ahead he sees another giant death robot scanner indicates that the angle of elevation from the top of Achilles robot to the top of the opposing robot is 4 degrees and the angle of depression to its feet is 30 degrees Give answer in exact vaules in terms of trig functions How far from Achilles robot is the other robot how tall is the other robot

holastic Student 15 17 V 8 U SRI College Career sin 1 8 15 m T Fossil Life An Intro PA cosine ratio should be used because it is the ratio sine ratio should be the length of the adjacent sid cosine ratio should be used because it is the ratid

QUESTION 10 Solve the problem A wire is fastened to a point T on a tree and to point ground The angle that the wire makes with level gro the wire is fastened to the tree Round to the nearest T

Question 4 25 points Law of Cosines At an airport radar tower the air traffic controller was able to determine how far two planes were away from the airport and the included angle How far were the two planes away from each other 2400 ft O 2800 feet 4000 feet 132 3200 ft

Draw a triangle if picture is not provided Round to the nearest tenth 10 A skateboarding ramp is 13 inches high and rises at an angle of 12 How long is the base of the ramp 11 Find the distance from A to C across the gorge illustrated in the figure

1 Solve for the unknown side 18 m 22 y 57 64 25 cm 14 mm 24 41 m

115 A shark is swimming 28 fe from a boat on the water t distance between the boat

A scoop from a bin of assorted jelly beans contained a mix of flavors root beer 5 licorice 22 cinnamon 6 What is the experimental probability that the next jelly bean scooped from the bin will be cinnamon jelly bean Simplify your answer and write it as a fraction or whole number P cinnamon

Find the error with subject verb agreement Select the incorrect verb and type it correctly Are neither basil nor rosemary in this dish Felix asked I m not tasting any herbs

Angles of Elevation and Depression 5 A hiker at the top of a mountain sees a farm and an airport in the distance 15 29 Farm What is the distance d from the hiker to the farm y T 5000 ft What is the distance y from the farm to the airport Airport Not drawn to scale What is the horizontal distance from the mountain to the farm

Each face on Mount Rushmore is about 60 feet high if look up at an angle of 6 to the top of one of heads and an angle of 4 to the chin how far from the base are you round to 1 decimal place

added a portable building The three steps that lead to the building rise 24 inches The school needs to put in a ramp to make the building wheelchair accessible By law the ramp must have an angle of elevation no greater than 15 The maintenance crew has a board they want to use to make the ramp The length of the board is 85 inches 16 in 24 in Part A Is the board long enough Use inverse trig to find x the angle of elevation of this board

Prove sinsin x y cos cos sinx casy secx croy x y sinx

x A flagpole is 50 feet from a point on the ground The angle of depression fr flagpole to the nearest foot

Which ratio represents sin A x x A B 17 15 17 8 C 17 8 B 64 17 D 15

35 95 rry is trying to calculate the height of a tower He is standing 95 meters from the b the tower is 35 Calculate the height of the tower to the nearest tenth of a meter

100 feet A tree that is 100 feet tall casts a shadow that is 150 feet long Determine the

Using electronic graphing tools graph y 2 sin 3 x 4 5 and y 2 csc 4x 3 1 on the same axes Find all points of intersection of the two functions between and with answers to 2 decimal places Include an image of the graphs in your response

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Question 20 wheel of an engine is 15 inches in diameter and the in diameter If the shafts of the drive wheel and the elt is required to join them as shown in the figure

3 24 Find the moment about point A for the lever shown in a Figure P3 24a and b Figure P3 24 30 N 70 30 N FIGURE P3 23 1 m A 3 m FIGURE P3 24a 70

An aircraft is spotted by two observers who are 2000 feet apart As the airplane passes over a line joining them each observer takes a sighting of the angle of elevation to the plane as indicated in the figure How high is the airplane 50 1000 ft 25

A soccer goal is 8 yards wide Suppose a goalie is standing on her line in the center of her goal as a striker from the opposing team moves the ball towards her The near post angle a is formed by rays extending from the ball to the near post and the goalie Similarly the far post angle is formed by rays extending from the ball to the far post and the goalie Determine the near post angle when the striker is 20 yards from the near post and 24 yards from the far post Near post B k Goalie 8 yd Far post

In circle L with m KLM 54 and KL 10 units find the length of arc KM Round to the nearest hundredth M L K