Heights & Distances Questions and Answers

Use a formula to find the surface area of the figure 11 in drawing not to scale A 287 in 2 QB 30 in C 574 in OD 858 in 13 in 6 in

3 Solve for x rounded to one decimal place 2 marks cos 59 36 Copyright 2019 The Ontario Educational Communications Authority All rights reserved

1 Convert each measure 4 marks a 8 ft 6 in to the nearest centimeter b 300 g to the nearest ounce

Find the value of the variables Lines that appear to be tangent are tangent b a 224 Input answer as a b

Simplify the expression to a polynomial in standard form 2x 1 x 6x 7

A cruise ship maintains a speed of 23 knots nautical miles per hour sailing from San Juan to Barbados a distance of 600 nautical miles To avoid a tropical storm the captain heads out of San Juan at a direction of 33 off a direct heading to Barbados The captain maintains the 23 knot speed for 8 hours after which time the path to Barbados becomes clear of storms a Through what angle should the captain turn to head directly to Barbados b Once the turn is made how long will it be before the ship reaches Barbados if the same 23 knot speed is maintained a The captain should head through an angle of Do not round until the final answer Then round to one decimal place as needed Barbados 33 San Juan

Question 3 Points 1 Which of the following shows the translation of K 3 2 two units down OK 3 2 OK 2 3 OK 3 0 OK 3 2

6 Jack bought an automatic water bottle feeder for his cat A diagram of the bottle is shown below What is the maximum amount of water that the bottle can hold 12 5 in 16 in 1 8 5 in A 238 07 in 3 B 328 07 in 3 C D 278 03 in 3 382 03 in 3

The circle at the right represents a planet The radius of the planet is about 6900 km Find the distance d to the horizon that a person can see on a clear day from the following height h above the planet h 2 km A person can see a distance of approximately km on a clear day from a height of 2 km above the given planet Round to the nearest tenth as needed E

A card is chosen at random from a standard deck Find each probability as a fraction in simplest form a decimal rounded to 3 places and percent rounded to the tenths place P ace Fraction Decimal Percent

You were asked to solve the A volleyball was hit into the air at a speed of 31 miles per hour at an angle of 35 from the horizontal Express this velocity in vector form Round your answer to four decimals Now that you have identified ul and cos 8 and sin 0 you can express the velocity in vector form using the fact that u Hullcos 0 lu sin 0 Find u cos 0 and lu sin 0 and enter your final answer for the velocity of the volleyball in the box below 31 0 35 U lucos 0 u sin

A skateboarder wishes to build a jump ramp that is inclined at a 19 0 angle and that has a maximum height of 32 0 inches Find the horizontal width x of the ramp Round your answer to one decimal place x

The height of a radio tower is 450 feet and the ground on one side of the tower slopes upward at an angle of 10 a How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 170 feet from the base of the tower b How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a point 170 feet from the base on the flat side a What is the length of the first guy wire feet Do not round until the final answer Then round to one decimal place as needed b What is the length of the second guy wire feet Do not round until the final answer Then round to one decimal place as needed 450 ft 170 170

5 12 23 7 14 AM Question 15 If QRST is a kite find QRS 279 A 164 B 79 C 101 D 137 R 11x 6 T S 4x 13

5 12 23 7 14 AM Question 13 In Circle W chords AC and DB intersect at Point J as shown below If AJ 12 JC 8 and BJ 6 what is JD A B 4 9 C 16 D 24 B 12 A 6 W C 8 Geometry Spring Final D Note The figure is not drawn to scale E A

Right triangle RST is shown below with the dimensions given in feet ft A B Which is closest to the measure of ZR C 15 1 15 7 S 74 3 17 ft T 63 ft R

A triangular prism has base edges 3 cm 5 cm and 7 cm long Its lateral area is 225 cm What is the height of the prism The height of the prism is Simplify your answer cm

5 4XYZ and AXYZ are similar triangle Find the value of d Y R X 50 50 S 98 98 30 40 32 d 32 32 T Z

1 Find the tree length ban 49 50 tree at so tan 6 1 free tree a 50 tan 49 5 a tan 61 a tan 49 5 tan 6 1 5 0 tan 49 5 49 5 50 dan 49 5 dan 49 5 tan 61 50 ft tree axtan6 1 16P 61 0 4marks tree

Calculator What is the value of x in the triangle Enter your answer in the box Round your final answer to the nearest hundredth 18 25 cm X

Calculator A party tent is used for an outdoor event Ropes of equal length support each tent pole The angle each rope makes with the ground is 55 What is the height of each tent pole Enter your answer in the box Round only your final answer to the nearest tenth MAN 25 ft 55

What is the value of x in this triangle Enter your answer as a decimal in the box Round only your final answer to the nearest hundredth X lo 29

Sam claims that cos X sin Y if X and Y are congruent angles Is Sam correct A Yes Sam is correct B C D No cos X sin Y if X and Y are corresponding angles No cos X sin Y if X and Y are complementary angles No cos X sin Y if X and Y are supplementary angles

Henry is painting a house He placed a 24 foot ladder 15 feet away from the base of the house so that it leaned up against the house Enter the measure of the angle that is formed between the ladder and the ground rounded to the nearest tenth

e parabolic arch shown in the ligure is 30 feet above the water at the center and 200 feet wide at the base Will a boat that is 30 feet Il clear the arch 68 feet from the center hoose the correct answer below O Yes 100 ft 100 ft 50 ft

A single six sided die is rolled twice What is the probability of rolling an odd number on the first roll and an even number on the second roll O A B 12 O c 1 4 O D 1 36

3 Write a trigonometric equation and solve to find x 24 12 gjo X

40 The number of ways to form a 12 person jury 41 The number of 6 digit passcodes possible from a pool of 40 potential jurors using the digits 1 8 if digits cannot repeat

Can someone please explain the steps with a diameter of 4 feet and a height of 9 feet This trough is conical in shape and is filled with a liquid that weights tbs per cubic foot The depth of the liquid is at 7 feet What is the amount of work in ft lbs that is required to empty the conical trough by pumping the water over the top

A boy is flying two kites at the same time He has a 350 ft of line out to one kite and b 430 ft to the other He estimates the angle between the two lines to be 30 Approximate the distance between the kites

A woman standing on a hill sees a flagpole knows is 70ft tall The angle of depression to the bottom of the pole is 14 degrees and the angle of elevation to the top of the pole is 18 degrees Find her distance x from the pole S 1945 2060 ing on a hill sees a flagpole that she knows is 70 ft tall The angle ce x from the pole Round your answer to one decimal place ft

A balloonist is directly above a straight road 1 8 miles long that joins two towns She finds that the town closer to her is at an angle of depression of 40 and the farther town is at an angle of depression of 38 How high above the ground is the balloon The balloonist is about miles above the ground 40 1 8 mi Not to scale answer to two decimal places as needed Round all intermediate values to four decimal places as needed

B x 2 E D x 5 x 12 C BE is 2 units longer than AE DE is 5 units longer than AE and CE is 12 units longer than AE What is BD units

Solve for x Round to the nearest tenth if necessary L 54 M X 58 K

Find the value of h for the parallelogram Answer 24 36

4 34 32

find the distance across a river a surveyor chooses points A and B which are x 200 ft apart on one side of the river see the figure She then chooses a reference point C on the opposite side of the river and finds that LBAC 82 and LABC 52 Approximate the cance from A to C Round your answer to the nearest foot ft A x ft 82 52 B

9 10 1 point What is the value of x x 1 point Find CD G 12 Type your answer 18 2x 7 11 D E

Look at the similar cones below Which statement must be true 15 36 25 60 The ratio to their volume must be 25 144 The ratio to their volume must be 27 125 The ratio to their height must be 1 3 The ratio to there surface areas must be 125 728 1 point The scale factor of two prisms is 7 3 Which could be the two surface areas 14 sq in and 6 sq in 147 sq in and 27 sq inches 49 sq in and 18 sq in 343 sq in and 27 sq in

A steep mountain is inclined 68 from the horizontal and rises to a height of 3200 ft above the surrounding plain A cable car is to be installed running from a point 930 ft from the base of the mountain to the top of the mountain The shortest length of cable places You can round the distance from the top of the mountain to its base to 5 3 additional decimal places or use the Ans feature on your calculator ft Round the final answer to 2 decimal

10 Scott set up a volleyball net in his backyard One of the poles which forms a right angle with the ground is 7 feet high To secure the pole he attached two ropes from the top of the pole to a stake 4 feet from the bottom of the pole Find the total length of the two ropes A 160 ft B 8 5 ft C 4 ft D 8 3 ft 10

Calculate the angle A in the following right angled triangle where a 53 2 m and b 5

sin u v x 1 Points DETAILS Use the figure to find the exact value of the trigonometric function sin

The height of a radio tower is 350 feet and the ground on one side of the tower slopes upward at an angle of 10 a How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 160 feet from the base of the tower b How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a point 160 feet from the base on the flat side

retractable awning above a patio lowers at an angle of 50 from the exterior wall at a height of y 11 feet above the round No direct sunlight is to enter the door when the angle of elevation of the sun is greater than 70 see figure What the length x of the awning Round your answer to two decimal places ft y ft 70 Suns rays

4 Find the height of triangle DEF 9 m B 11 m E 13 m

Because of prevailing winds a tree grew so that it was leaning 6 from the vertical At a point d 40 meters from the tree the angle of elevation to the top of the trees is a 28 see figure Find the height h of the tree Round your answer to one decimal place h

maximum safe incline for a ramp is B 5 degrees Is this ramp safe If not provide dimensions that would make the ramp safe 95 15 Hide Transcribed Text 4 Lesson 9 Practice Problem Ramps in a parking garage need to be both steep and safe The maximum safe incline for a ramp is 8 5 degrees Is this ramp 2 TS

Geometry 3 A car dealership sells new and used cars SUVS and trucks They recorded the type of vehicle and whether it was new or used for the past 200 sales Complete the missing joint and marginal frequencies in the table below Type of Vehicle Car SUV Truck Mikayla Morris Two Way Tables Practice pdf Total New 41 124 New or Used Used 36 16 Total 91 65 4 Create a relative frequency table using the table from 3 by filling in all joint and marginal relative frequencies Type of Vehicle Car SUV Truck Total New New or Used Used Total

For a project in her Geometry class Hailey uses a mirror on the ground to measure the height of her school s flagpole She walks a distance of 11 15 meters from the flagpole then places a mirror on flat on the ground marked with an X at the center She then steps 1 35 meters to the other side of the mirror until she can see the top of the flagpole clearly marked in the X Her partner measures the distance from her eyes to the ground to be 1 55 meters How tall is the flagpole Round your answer to the nearest hundredth of a meter 1 55 m 1 35 m 11 15 m Diagram is not to scale