Heights & Distances Questions and Answers

50 ft to mi and sees a mirror on the ground m the mirror to practice her Geometry the height of the school She also kn the school from a previous Geometry distance she is standing from the mir

1 In AABC mzB 90 and AB CB and BC 5 3 Determine the length

X A D 20 X 4 he diagram segment AD bisects angle BAC en the following segment lengths the value of x and to the nearest tenth

person shadow nd his shadow is 4 ft long The tree s shadow is all your work

blem 5 a Let u 9 1 6 6 and v 9 1 1 6 Find u proj u Note You can partially check your work by first calculating proj u and then verifying that the vector proj u and u proj u are orthogonal

1 The accompanying diagram shows a ramp leaning against a wall where the ramp meets the wall at a height of 24 feet If the distance from the bottom of the ramp to the wall is 28 feet determine the angle x that the ramp forms with the ground X nearest tenth of a degrest

In May of 1937 American aviation pioneer Amelia Earhart attempted to circumnavigate the globe According to flight logs the first stage of the trip was 110 nautical miles less than the second stage of the trip and the two stages combined totaled 676 nautical miles How many nautical miles was the first stage A 249 B 283 C 327 D 390 Postedal

4 40 D your path brother s path 60 ft A to across the pool how far apart will you be when you both get to the other side Hint Solving for length of line AC F O Submit

Find the outer perimeter 10 ft 20 ft 15 ft Remember Co 2 r P ft Round to the nearest hundredth Use 3 14 for T

13 Two guide wires support a flagpole FH The first wire is 11 2 meter long connecting of inclination of 39 The second wire has an angle of inclination of 47 and connects FG How tall in the flagpole LU E 47 39 11 2 m G mol fusibaslamia ni

11 A student sees a bird on top of a 12m high light pole The student is standing 20m from the base of the pole At what angle must the student incline her camera to take a picture of the bird a 31 c 59 0 b 37 d 87

1 In the diagram below of right triangle ABD the mzB 90 Determine to the nearest whole meter the distance from D to C A 45 100 m D x m C B

9 Using the diagram below find the angle of elevation of a kite on a 50m string flying 40m vertically above the ground to the nearest tenth A 64 2 B 45 6 C 23 9 D 53 1 50 m 090 40 m

P Question 6 M Name two points of tangency 3 pt

Show ALL of your wo 1 Two guide wires support a flagpole FH The first wire is 11 2 meter long and of 39 The second wire has an angle of inclination of 39 How tall in the flagpole U 47 39 11 2 m G H as all

14 To answer questions 12 17 use the formulas for functions of the differen and sum of two angles to find without tables or calculator the cosine si and tangent of the angle 15 using 45 and 30 cos 15 A cos 45 cos 30 sin 45 sin 30 sin 45 cos 30 cos 45 sin 30 OC cos 45 cos 30 sin 45 sin 30 OD sin 45 cos 30 cos 45 sin 30 B

16 To answer questions 12 17 use the formulas for functions of the difference and sum of two angles to find without tables or calculator the cosine sine and tangent of the angle 15 using 45 and 30 tan 15 A 1 tan 45 tan 30 tan 45 tan30 OB O C O D tan 45 tan 30 1 tan 45 tan 30 tan 45 tan 30 1 tan 45 tan 30 1 tan 45 tan 30 tan 45 tan30

7 Given tan 24 tan 21 what is the value 1 tan 24 tan21 O A 1 OB 1 O C 0524 D 19 08

From a hot air balloon Mariana measures a 40 angle of depression to a landmark that s 1165 feet away measuring horizontally What s the balloon s vertical distance above the ground Round your answer to the nearest hundredth of a foot if necessary

In order to determine the width of a river a surveyor made this sketch of similar triangles from measurements he made along a river OB 120 ft O What is the distance across the river from point A to point T OA 84 9 ft C 69 3 ft AM D 60 ft A 120 ft B 80 ft U D 40 ft C

INDEPENDENT 2 In the diagram above of right triangle ABD the mzBAD 60 Det the distance from D to C A 450 600 100 mt

A surveyor measured the road frontage of a parcel of land and obtained a distance of 18 72ft Based on this result the distance must be between what two values The distance must be at least ft

X tangent 65 17 cosine Which ratio would you use to solve for x hypotenuse sine

B 10 m 2 m inverse cosine Which inverse trig function would you use to find the measure of Angle A inverse tangent inverse sine It is not possible to determine m A

7 Q 45 Sine Choose the correct trig function Tangent t Cosin

57 Write 6 as a decimal number 100 Submit

For this project you will create a children s book that explains how to do a problem you have created involving trigonometry The audience for your book is a group of your peers To create your book do the following 1 Create a fictional story problem that must be solved using trigonometry All values used in your problem should be realistic Your problem should also be relevant to the life of a teenager 2 Solve your problem 3 Write a fictional story around your story problem Your problem should be part of the story not just inserted into a fictional story line Your story must have at least 2 characters and must explain the following a Why your characters are trying to solve the problem b How they you solve the problem in detail 4 Your story must include the work you did to solve your problem either in the text of the story or the pictures that accompany the text or both Your book should be created by using PowerPoint Presi or another program of your choice Your books should have pictures and be colorful Make sure you book contains the following elements Cover Title Page Story About the Author You should be as creative as possible with this

8 4x 3y 3 4x 3y 7 10 6r 312 12

a EVERYBODY WRITES Write the segment subtraction statement we will use to solve for A b Solve for the value of B 115 56 X 35 C

2 A lighthouse is built on the edge of a cliff near the ocean as shown in the accompanying diagram From a boat located feet from the base of the cliff the angle of elevation to the top of the cliff is and the angle of elevation to the top of the lighthouse is Determine the height of the lighthouse to the nearest tenth of a foot 1801280 200 ft 4 x Cliff

1 In the diagram below determine the value of to the nearest tenth 119 70 X 26

1 A certain part of a hiking trail slopes upward at about a angle 5 yft 100 ft x ft a After traveling a horizontal distance of feet along this part of the trail what would the change in a hiker s vertical position b What distance has the hiker traveled along the path

43 22 10 X 11 3 Find the length of side x 12 0 15

42 16 Name Geometry Project 2 Parallel Lines and Transversals 7 Use the diagram below to answer questions 1 10 Line m is parallel to line n I is a transversal 3 5 6 8 1 2 Block 4 m Spring 2023 72 Label the following angle pairs as corresponding vertical alternate exterior or alternate interior 1 25 and 27 6 22 and 23 2 22 and 26 7 t and 25 3 23 and 26 8 41 and 44 4 41 and 28 9 24 and 28 5 23 and 27 10 42 and 47 11 Find the measures of the following angles if the measure of Z 1 is 120 degrees

A D 4x 9 15 B C Figure 2 I assume a student might believe Segment BC is a Tangent how do you know it is a Tangent O In my heart of hearts I believe point C to be the point of tengency O Cuz it looks like aTangent O Because the intersection at point C creates a 90 O What would you call it

3 SAT Question Ratios Rates and Proportions A rolling ball covers a distance of 2400 feet in 4 minutes What is the ball s average speed in inches per second 12 inches 1 foot

How many tangent lines can you draw from point A to a given circle B OC B 3 1 2 4 A

Two different cross sections are taken parallel to the base of a three dimensional figure The two cross sections are the same shape but are not congruent Which could be the three dimensional figure Select three options Students if you believe you earned partial credit on this problem please reach out to your teach cylinder square pyramid triangular prism triangular pyramid

receive full credit 1 In the diagram below the angle of depression from the top of the lighthouse to a speel lighthouse is 33 ft Determine the distance between the base of the lighthouse and the boat A MathBits com C B

The angle of elevation from a point on the ground to the top of a pyramid is 24 50 The angle of elevation from a point 110 feet farther back to the top of the pyramid is 13 10 Find the height of the pyramid What is the height of the pyramid ft 110 13 10 24 50 X

6 An observer is 120 feet from the base of a television tower which is 150 feet tall Find to the nearest degree the angle of elevation of the top of the tower from the point where the observer is standing 4 pts

City A is 350 miles due south of City B City C is 500 miles due east of City B What is the measure of Zc to the nearest degree 8 350 miles 35 44 55 90 500 miles

M 14 Solve radical equations EHE Solve for g g 4 10 g

In a circle with center C central angle XCY has a 3 T measure of radians The major arc XY formed 2 by central angle XCY is what fraction of the circumference of the circle

y2 12x 384 y 4x In the xy plane if a point with coordinates f g lies in the solution set of the system of inequalities abov what is the minimum value of g

Directions Solve each problem Crcle the answer that matches your solution Color the Purple your selected answers Colors may be used more than once Staple all work to this paperl Orange What is the sum of the measures of the Interior angles of a 23 gon 3 460 3 620 2 What is the measure of each Interior angle of a regular 18 gon 3 What is the sum of the measures of the exterior angles of a dodecagon 4 What is the measure of each exterior angle of a regular 20 gon 5 If the sum of the interior angles of a polygon is 1 980 how many sides does it have 6 If an Interior angle of a regular polygon measures 144 how many sides does it have 7 If an exterior angle of a regular polygon measures 15 how many sides does it have Black 40 Yellow 270 Pink 18 Yellow 13 Light Blue 8 Orange 23 Brown 160 Light Green 320 8 If the measures of a heptagon are 127 152 12 123 135 Light Green and 105 what is the measure of the remaining angle 138 Dark Blue 25 Gray 14 Purple 9 Dark Green 3 780 Dark Blue 24 Orange 146 Light Blue 190 Red 360 Orange 162 Yellow 15 Gray 10 Pink 25 Black 154

0 in 2 in 4 in S 3 in 189 2 in 3 in 2 in 5216 cubic 12 in cubic in Fall 6 in 192 cubic 8 in Instructions 2 12 in 3 7in 10 in

Classify this polynomial 4u quadratic Submit linear cubic none of these

Xin leans a 26 foot ladder against a wall so that it forms an angle of 78 with the ground What s the horizontal distance between the base of the ladder and the wall Round your answer to the nearest hundredth of a foot if necessary

4 An object dropped from the top of the Leaning Tower of Pisa lands 17 ft away from the base a Which equation can be used to determine the angle that the Tower makes with the ground A cos x 179 Work B COS X 179 17 C sin x 17 179 b Determine the measure the Tower makes with the ground to the nearest whole number Method D sin x 179 17 179 ft