Heights & Distances Questions and Answers

In order to image small objects with high resolution select all possible methods Lower electron gun current Use a smaller spot size Move up the specimen closer to the objective lens Increase the accelerating voltage Increase the image contrast

To avoid charging effect in SEM imaging select all possible methods Coat with metals Coat with carbon Decrease the voltage Decrease the chamber vacuum Use a larger aperture

height of the Eiffel Tower Antoine placed a mirror 500 meters away from the tower He then positions himself as shown so that the top of the tower is visible in the mirror He is standing 2 75 meters from the mirror and his eyes are 1 8 meters off the ground How tall is the tower

5 Proof by smallest counterexample Prove the following using smallest counterexample 6 n n21 for every positive integer n Note that we will cover proof by strong induction in the number theory homework 00 You got this

Use a calculator to evaluate each function Round your answers to four decimal places Be sure the calculator is in the corred angle mode a cos 8 50 29 b sec 56 20

ap16Sec1 003 pg The figure below shows contours of g x y on the region R with 3 x 9 and 2 y 8 1 3 Using Ax Ay 2 find an overestimate and an underestimate for g x y dA

Find the EXACT lengths of the missing leg and hypotenuse A note on EXACT answers If your answer has a radical for example leave the radical in your answer If it is fraction don t round it as a decimal 8 m 45 n

E A B In the pentagon ABCDE LA ZB 90 ED DC AE BC Four points are marked on AB dividing it into five equal parts Then perpendiculars are drawn through these points as shown in the diagram The dark shaded region has an area of 13 cm and the light shaded region has an area of 10 cm What is the area in cm of the entire pentagon A B C E 45 47 49 49 58 60

A paper airplane was thrown from a height of 25 feet and descends at an angle of 28 to level ground How far away on the ground will the paper airplane land from where it was thrown

In 10 11 Use the appropriate trigonometric function to find the value of x in each triangle round sides to the nearest tenth and angles to the nearest degree Don t forget units 10 A kayaker makes a 16 angle of elevation to the top of a lighthouse The kayaker is 110 meters from the base of the lighthouse find the line of sight distance from the kayaker to the top of the lighthouse Kayaks 16 X Top of lighthouse Entrance to bay

Describe each angle as an angle of elevation or angle of elevation or depression 9 21 23 22 24

METRY Unit 8 Test 1 Complete using hypotenuse opposite and adjacent Sin A Cos A A Sin A Cos

In 12 14 Use the appropriate trigonometric function to find the missing value round sides to the near tenth and angles to the nearest degree Don t forget units 12 Bobby hides behind a rock 42 3 meters from the south end of a pond His opponent s flag is flying at the north end of the pond How far does he have to run from the rock to point A to capture his opponent s flag 30 42 3 m

A boy stands 6 meters away from a building His line of sight forms a 78 angle of elevation to the top of Iding Find the total height of the building if his eyes are 1 2 m from the ground 11

13 An airplane starts its descent towards an airport when its horizontal distance is 52 800 ft from the runwa and the line of sight distance is 54 500 ft Find the airplane s angle of descent depression 52800 ft 54500 ft

48 8 X

6 Vanessa Samantha Hannah and Jordyn are all part of a 12 member volleyball team Four members of the team are randomly selected to fill the water jug for the day What is the probability that all four of them will be chosen Lesson 21 3 1 5 points

Pernside Nying 3 You have a set of 10 cards numbered 1 to 10 You choose a card at random Event A is choosing a number less than 5 Event B is choosing an even number Calculate the probabilities of the following a P A d P A S 5 1 b P B 3 A 2 4 B 6 e P BC 7 10 8 TOWER 9 VELL c P ANB 4 You roll a 6 sided number cube Use the complement to determine the probability of not rolling a 4 12ES140 SE 5 A bag contains 2 red 5 blue and 3 green balls A ball is chosen at random Use the complement to determine the probability of not choosing a red ball Optional Complete problems 1 9 11 13 15 18 19 23 26 odd from your textbook on separate lined paper

R S 45 cm 22 45 cm T

The world s tallest flagpole is 282 ft tall The shortest shadow cast by the pole is 137 ft long Find the angle of elevation from the tip of the shadow to the top of the flagpole

In 11 13 Draw a picture for each problem then solve 11 A person standing 30 feet from a water tower can see the top of the tower at a 55 angle of elevation person s eye level is 5 feet from the ground Find the height of the water tower

A boat is sailing about 400 ft from the cliff at the shore of a lake A sailor on the boat uses a device to measure the angle of elevation between the lake level and the top of the cliff Find the height of the clif 15 Cliff h

5 An airplane is flying 31 yards above the ocean Find the angle of depression from the plane to the boat when the plane is a horizontal distance of 50 yards from the boat X 31 yd

7 10 H D P V y 60 8 X y 60 go y 7 30 X bi X 5 6 3 60 X 17 9 y y

4 15 3 4 5 5 X 4 6 x S

2 20 13 in

9 16 yd 15

37 3 yd X

ric Summary 3 points 1 m2CAB 1 m2DAB 1 conclusion reasoning A h 5 14 0 B 0 Cos123 53 13 A 4 in 3 O 10 B 3 d a Your friend gives you the right triangle above and to the left and says Bisecting an angle is really easy Take triangle ABC If I wanted to bisect ZCAB all I need to do is find the midpoint of BC The ray that goes from A through the midpoint of BC will cut ZCAB in half because it cuts the side BC in half Your friend then sketches the triangle above and to the right so that point D is the midpoint of side BC Convince your friend that they are wrong Use trigonometry to show that ZDAB and CAD are not congruent Show all work Use complete sentences to explain your conclusion and reasoning

16 10 in 6 in 17 in 17 2 5 ft 24 ft X 18 4 m 3 6 m 12 m

6 1 point The pentagon shown could be reflected over which line to be carried onto itself x axis y axis line y x not possible