Heights & Distances Questions and Answers

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

Using the drawing below determine the height of the tree to the nearest tenth of a foot The horizontal distance from the base of the tree to the point of the angle of elevation is 95 feet 80

Find z 13 6 30 N 60 Write your answer in simplest radical form

Triangle ABC is a right triangle Point D is the midpoint of side AB and p D B 68 E The proof with a missing reason proves that the measure of ZECB is Statement mLADE 68 Given Definition of a right angle Triangle Sum Theorem m2DAE 90 m2AED 22 DE joins the midpoints of AB and AC Given DE is parallel to BC ZECB ZAED m2ECB 22 Reason Corresponding angles are Substitution property

Express cos V as a fraction in simplest terms U 10 T 25

Strategic Management relates a study in economies of scale in the paper industry the data is found in the following table 50 60 73 82 90 215 230 260 1 8 1 6 1 5 1 25 0 95 0 60 0 50 0 54 Here x is the weighted average machine size in tons per hour and y is the employee hours per ton A Determine the best fitting line using least squares and the square of the correlation coefficient The best fitting line is W x The square of the correlation coefficient is 2 B Is there an advantage to using a large machine Pick the correct answer The larger the machine the more the employee hours The smaller the machine the less the employee hours The larger the machine the employee hours do not change The larger the machine the less employee hours C What does this model predict the weighted average machine size will be is the employee hours per ton is 1 00 Round to the nearest ton The machine will make tans for 1 employon bour

The table shows the total personal income in the United States in billions of dollars for selected years from 1960 and projected to 2024 Year Income billions Year Income billions 1960 411 5 2008 12 100 7 1970 838 8 14 728 6 1980 19 129 6 22 685 1 2307 9 4878 6 8429 7 2014 2018 2024 1990 2000 a These data can be modeled by an exponential function Write the equation of this function with x as the number of years past 1960 and y as the total personal income in billiom Round your numerical values to three decimal places y b Does the unrounded model overestimate or underestimate the total personal income given in the table for 2018 The model overestimates the projected total The model underestimates the projected total c Graphically determine the year the model predicts total personal income will reach 63 trillion

Select the statement used to prove that AB A D 12 Show your work here 30 E 30 B O AABD ACDB by the ASA criterion O AABE ACDE by the ASA criterion O AABD ACDB by the SAS criterion 12 O AABE ACDE by the SAS criterion G

DIRECTIONS Type your answer in the space provided In this isosceles trapezoid below what is the measure of L K N 66 M

Find the value of s in rhombus HIJK J I 2s 90 4s 18 H

Look at this diagram I L O M 3 H K N If IK and LN are parallel lines and m LMJ 130 what is m JH

A plane is flying at a constant altitude At a moment in time the angle of depression from the center of the plane to the base of the control tower is 18 degrees After the plane flies 3 miles toward the control tower at the same altitude the angle of depression is now 22 degrees At what altitude in miles is the plane flying Not drawn to scale 5 miles

Previous P 1 point A his shadow Your answe Hint Draw

points Use the figure below to complete the statements 1 3 W X If m XYP m YXP If PX PY 4 2 Y

2 d 22 out of The mean height of the 2018 Women s W o Sue Bird 5 9 O Tina Charles 6 4

Determine dimension d in the accompanying figure to two decimal places 8 150 16 350 9 250 33 50 d

1 Solve for the value of y below to the nearest CI 11 en Xar the lice have been called to ac of Liberty The victim is ue 28 As y lice talk to the witnesses they gather 5 The crime unit has been unable to decipher th elp Each clue

Two fire lookout towers A and B are located 3 km apart on a straight road A fire was observed from both towers From A the angle formed between the road and the fire was measured to be 40 From B the angle formed between the road and the fire was meassured to be 56 50 Find the distance between tower A and the fire Round your answer to 1 decimal place Distance in km Number Fire

Is the quadrilateral a parallelogram Why or why not 65 115 OA No the opposite angles are not congruent OB No we would need to know about the other sides or angles OC Yes the angles are supplementary OD Yes the angles show that the congruent sides are parallel

14 Solve for x Round answers to the nearest hundredth 32 4 OA 36 81 OB 24 15 OC 27 82 OD 20 99

13 Determine the reference angle of 240 A 30 B 60 C 45 D n a

10 cosB Determine e f g h 3 HIN 1 2 the value of tanB 3 2 2

Which letter has point symmetry OAT OBH OCA

8 Find the value of the indicated trigonometric function of the angle in the figure Give an exact answer with a rational denominator Find tan 8 O tan 8 A B D 8 tan 8 617 7 8 tan 8 8 tan 8 B 113 8 113 7 7

The diagram below shows an angle with an unknown measure of radians and a circle with Us 2 3 The terminal point is 1 18 cm above the circle s center Measurement d What is the value of cac 0 a What is the measure of the terminal point s distance above the circle s center in units of the radius of the circle Measurement Preview b What is the value of sin 0 0 e What is the value of 0 23 cm sin 0 Preview c What is the measure of the radius of the circle in units of terminal point s distance above the circle s center Preview Preview 18 cm Preview ong cemereu atunc

7 Find the length of the missing side of the right triangle below If necessary round to the nearest tenth 16 20 OA 12 OB 26 6 OC 144 OD 4

TIVITE Homework The dimensions of a rec a the volume of water in b the number of kilolite water

16 The person in the picture sight If the angle the person is lookin

A radio tower was built in two sections From a point 87 feet from the base of the tower the angle of elevation of the top of the first section is 25 and the angle of elevation of the top of the second section is 40 To the nearest foot what is the height of the top section of the tower Maths com 87 feet 40 25

Solve sin x 0 55 on 0 x 2 There are two solutions A and B with A B A B 11

A plane flying with a constant speed of 9 km min passes over a ground radar station at an altitude of 14 km and climbs at an angle of 40 degrees At what rate is the distance from the plane to the radar station increasing 3 minutes later The distance is increasing at km min Hint Hint The law of cosines for a triangle is where is the angle between the sides of length a and b e a b 2abcos 0

Learning Math Reveal Math 8th grade Q 17 Transversals of parallel lines LN and OQ are parallel lines O Language arts R P M N Q

na is supported by two wires 165 ft and 180 ft long Each the top of the antenna and secured to the ground on opposite sides of the antenna The shorter wire makes an angle of 67 with the ground a Sketch and label the triangle b Find the height of the antenna Give both an exact test answer and a calculator approximate answer c How far apart are the antenna bases on the ground You ll need a calculator here

Consider the quadratic function f x 2x 8 24 Determine the following enter all numerical answers as integers or decimals Round your answer to two decimal places as needed The T intercept s are Write the answer as two ordered pairs separated by a comma The y intercept is Write the answer as an ordered pair The vertex is Write the answer as an ordered pair The line of symmetry has the equation

Question 10 of 10 a payday loan for 1500 that Which will have a higher effective interest rate is due in 12 days with a fee of 90 or a payday loan for 1500 that is due in 10 days with a fee of 90 A A payday loan for 1500 that is due in 10 days with a fee of 90 since it has the shorter period OB A payday loan for 1500 that is due in 12 days with a fee of 90 since it has the shorter period OC A payday loan for 1500 that is due in 10 days with a fee of 90 since it has the longer period D A payday loan for 1500 that is due in 12 days with a fee of 90

Question 9 of 10 Pete has the option of borrowing 380 for one week at an APR of 600 or borrowing the 380 for one week with a fee of 45 Which is the better deal OA Borrowing the 380 for one week at an APR of 600 since Pete will owe less interest this way than with the fee of 45 OB Borrowing the 380 for one week with a fee of 45 since Pete will owe more interest this way than with the 600 APR OC Borrowing the 380 for one week with a fee of 45 since Pete will owe less interest this way than with the 600 APR D Borrowing the 380 for one week at an APR of 600 since Pete will owe more interest this way than with the fee of 45

The side length of each cube is inch What is the volume in cubic inches of the right rectangular prism 14 16 12 x 23 B 48 320 x 366 3312 3312in Denzel has two stacks of identical storage boxes in his room One stack has 3 boxes and the other stack has 5 boxes The volume of the stack of 3 storage boxes is 11 cubic feet The drawing shows the stack of 3 storage boxes F1 12 2 feet 211 968 2 feet cubes t A at is the height in feet of 1 storage box

two circles are tangent and inscribed in a larger circle A line through their tangent line is 6 inches What is the shaded area left outside the two circles

A tree on a hillside casts a shadow c ft down the hill If the angle of inclination of the hillside is b to the horizontal and the angle of elevation of the sun is a find the height of the tree Assume a 55 b 25 c 245 ft Round your answer to the nearest whole number

Ing the motion of Venus is correct Explain FIVE PHASES OF VENUS 5 1919 SEPT 25 Joplo o 4 At what phase does the Earth appear to be in as seen from Venus during each of its phases in Part 2 Now in general compare the phases exhibited by an inner planet to those exhibited by an outer planet in the heliocentric theory Porin o JUNE 19 Venus takes 225 days to go around the Sun yet Venus takes more than 225 days to go from one new phase to the cat new phase as seen from the Earth Why is this explain the observed phases of Venus using the Challenge See if you can imagine a way model which you concluded to be incorrect

What is the letter that designates slope

Solve the right triangle F 330 71 E

Identify the expressions equivalent to sin 74 given the triangle Please select two Show your work here 33 cos 16 72 cos 74 75 74

YA 2 0 2 y f x 4 6 f where does F have a maximum value A minimum value g What is the average value of f x on 2 9 8 16 The graph of fis shown above If F x f 1 dt evaluate the following using areas to help you a F 0 b F 2 C F 5 d F 7 F 5 e F 9 X

8 Two mountain peaks R and T can be observed from an alpine meadow To estimate the straight line distance between the peaks members of a hiking party measure out 500 m baseline AB in the meadow where A B R and T are in the same plane on the same side of the mountain The angles from A and B to the peaks are then measured and ZBAR 155 ZBAT 33 ZABT 145 and LABR 21 Determine the distance RT to the nearest 10m

Find the measure of angle b in degrees Round to two decimal places as necessary 25 Show your work here 26 b

A fireman is standing 30 m directly west of a burning building His ladder reaches 50 m up the side of the building What is the angle of elevation to the nearest degree of his ladder A 48 58 c 59 D60 61