Solution of triangles Questions and Answers

3 7 1 8 Solve for the missing side length If using Pythagorean Theorem Pound your answers to the nearest 100th If the triangle can be solved using a special right triangle Patio leave answer as a simplified Radical X D 14 60 X 30 X 8 17 8 X 20 2 4 8 12 45 X 3 2 X X 8 D 30 45 9 10

7 10 MIX Pythagorean Theorem 45 45 90 30 60 90 Solve for X 7 9 45 30 8 X X 5 5 8 10 15 X 16 2 x

5 8 Solve for x and y Leave answer as a simpll 6 5 7 9 X A 45 6 4 45 X 45 10 2 X y 45 Y 45 T X 5 2 10 3 2 hi Y X 16 X 45

HW 8 1A 14 Find the length of the missing side Found 2 decimals when necessary Show 3 1 X 5 2 5 X 12 4 X 3 6 10 9

Pationalize JLN 3 4 Multiply 157 2 2

Question 10 1 point y Solve for x O a Ob Oc Od 3 6 30 X 3 2 3 3 6 3

Question 8 1 point X 60 Solve for x O a 5 3 Ob 5 3 Oc Od 10 3 10 5

4 2 Solve for y O a Ob Oc Od X 4 8 point y 45 4 2 8 2

A telephone pole breaks and falls as shown To the nearest foot what was the original height of the pole A 18 ft B 16 ft C 17 ft D 19

Sketch a triangle that has acute angle 0 and find the other five trigonometric ratios of 0 35 cos 0 37 Step 1 Cosine in terms of the right triangle is defined as the adjacent This means that the hypotenuse of the triangle is 37 x 35 X 37 1225 I over hypotenuse C and you can solve for the missing side using the Pythagorean Theorem Simplify your final answer

Solve the triangle if a 18 m b 34 m and c B Y 0 O 33 m Assume Za is opposite side a ZB is opposite side b and Zy is opposite side c Enter your answer as a number answer should be accurate to three decimal pla

7 Given the information provided in the diagram and that angles and ZABC and ZABD are right angles determine the measurement of CAD 12 15 110 16

Find the reference angle for the given angle a 255 b 460

Find the angle between u 4 5 and v 5 4 to the nearest tenth of a degree The angle between u and v is 167 3 Round to the nearest tenth

Which of the following equations when graphed in the xy plane will include only values of y that are less than 2 A y x 3 B y x 1 C y x 4 D y x 1 1

In the xy plane if 1 0 is a solution to the system of inequalities y x c and y x d which of the following must be true about c and d A c d B c d C c d 5 d c

At 12 P M on Sunday there are 25 000 people in a football stadium that holds 65 000 Every minute after 12 P M the number of people in the stadium increases by 550 If m represents the time in minutes after 12 P M which of the inequalities below gives the set of minutes in which the football stadium is below capacity A 550m 25 000 B 550m 65 000 C 550m 25 000 65 000 D 25 000 550m 65 000

Income in dollars Under 25 000 25 000 49 999 50 000 74 999 75 000 99 999 100 000 and above Total Under 19 12 499 15 624 14 061 10 936 24 998 78 118 Number of United States Residents With Health Insurance in 2015 in Thousands Age in years 19 25 4 881 6 102 5 491 4 271 9 762 30 507 26 34 6 146 7 683 6 915 5 378 12 293 38 415 P Time heart 35 44 6 387 7 984 7 185 5 589 12 774 39 919 65 and older 13 314 7 359 16 643 9 200 14 978 8 278 6 439 45 64 11 650 26 628 83 213 14 718 45 994 Total 50 586 63 236 56 908 44 263 101 173 316 166 The table above shows the number of U S residents with health insurance in 2015 in thousands categorized by age group and annual income According to these results if a U S resident with health insurance who was 35 64 in 2015 s selected at random what is the approximate probability that this resident had an income between 50 000 and 574 999 0 20 B 0 25 C 0 40

tan i tan ne formula D 24 1 A 1 os tan i tan must be expressed in radians pproximate the number of hours of daylight in a city at 30 45 north latitude on a the summer solstice i 23 5 b the vernal equinox i 0 and c July 4 i 22 48 cos can be used to approximate the number of hours of daylight when the declination of the Sun is i at a location 0 north latitude To use the The number of hours of daylight on the summer solstice is hours o not round until the final answer Then round to the nearest hundredth as needed

Owen is rowing a boat gently down the stream The length of the oar from the side of the boat to the tip of the blade is c 8 feet At any given moment the oar makes an angle with the side of the boat as indicated in the figure Determine the angle when the tip of the blade is positioned at a distance of b 6 feet from the boat Write your answer in degrees Round to two decimal places if necessary cft bft

School Supplement 4 Sixty percent of the campers at Camp Sunshine are boys Thirty percent of these boys are 13 years old What percentage of the campers at Camp Sunshine are not 13 year old boys

5 XE 0 2 olmak zere tanx cot3x 1 denkleminin dir A z m k mesi a a dakilerden ha D 0 2 T B 0 1 c 0 E 0 2 2n 1 3 1

Write an equation for the quadratic graphed below Round all values to two decimal places as needed x intercepts 1 0 and 2 0 y intercept 0 2 0 2 2 0 a

Graph the function using the given viewing window Find the intervals on which the function is increasing or decreasing and find any relative maxima or minima Change the viewing window if it seems appropriate for further analysis f x 1 3x 5 9x 3 97 4 4 8 14 Choose the correct graph below OA G OB M Q L OC N Q Q 2 O D W Q Q 5 On what interval s is the function increasing Select the correct choice below and if necessary fill in the answer box within your choice OA The function is increasing on the interval s Type your answer in interval notation Use a comma to separate answers as needed Round to three decimal places as needed OB The function is never increasing On what interval s is the function decreasing Select the correct choice below and if necessary fill in the answer box within your choice

aculty at a certain university need to create a committee to evaluate the general studies curriculum offered on campus If there are 24 faculty members and they must select a chair vice chair secretary and 3 additional faculty members to be on the committee in how many ways can the committee be formed Number of possible groups

Find the value of x 31 to 30 x 0

Use your knowledge of all triangles to find the value of the variable Round SIDE lengths to the nearest tenth and ANGLES to the nearest degree X y

Show how you will find the remainder when 20 5x 3 is divided 3 by using synthetic division DRAG DROP THE ANSWER 1 6 x 3 1 3 2x 1 0 3 2 2 3 5 6 Divisor Quotient O Remainder

Express D as a B 4 3 I simplest D

Let f x 4 x If g x is the graph of f x shifted down 3 units and right 6 units write a formula for g x g x Entor la no cortlyd

Describe a function g x in terms of f x if the graph of g is obtained by vertically stretching f by a factor of 9 then shifting the graph of f to the right 7 units and upward 2 units g x Af x B C where A B C

Express cos S as a fraction in simplest terms 29 R 8 S

Find the value of sin D rounded to the nearest hundredth if necessary B D 10 24 C

Which segment is opposite to ZX XQ OXZ X Z

Consider the triangle below b a 45 13 5

d linear pairs are supp and tanB 0 3 9 In the triangle to the right sinA H 5 opposite sides different Explain using vocabulary 0 A 11 tim 4 3 Why are the A 5 in 4 in 3 in C

for x Y 2x 3 R ON x 2 STOP OFF RESET 0 X 4 FIX 2 5 8 3 ANS 6 9 11 ENTER 1 X R 12 S AE x 1 X 6

Given B and C form a linear pair A B and m A 12 Prove mzC 60 Stots

Given B and C form a linear pair A B and mzA 120 Prove m C 60 Statement 1 A B 2 m A mzB 3 m A 120 4 120 m B 5 B and C form a linear pair 6 mzB m C 180 7 120 mzC 180 8 m C 60 Reason 1 Given 2 3 Given 4 Substitution 5 Given 8 6 Linear Pair Postulate 7 Substitution Select the reason that best supports Statement 2 in the given proof A Reflexive Property B Definition of Congruency C Linear Pair Postulate D Subtraction Property of Equality

2 In the diagram below mzB 90 and AB 2 and AC 10 A Determine the length of BC in simplest radical form B

2 In the diagram above of ADEF a Determine the length of DF b Determine the sin D and the sin F YOU DO ROUND 2 8 cm F 3 cm

3x 2 B 16 10 E For what value of z is DE a midsegment of Iriangle ABC A05 B O c 06

Find the missing length indicated O 120 O 20 64 O 16 O 100 48

James wants to draw a line diagonally across a rectangular piece of paper If the paper measures 9 inches by 12 inches what is the minimum length of the straight edge he needs to make the line O 15 inches O 21 inches O None of the other answers are correct

Find the missing length in the right triangle 6 ft O 10 ft O 12 ft 8 ft Nong of the other answers are correct

Find the missing length indicated 9 O 100 O 20 O 16 O 60 12 X None of the other answers are correct

A baseball diamond is actually a square with sides of 90 feet If a runner tries to steal second base how far must the catcher at home plate thrown to get the runner out Round your answer to the nearest hundredth feet

9 A soccer field is a rectangle 90 meters wide and 120 meters long The coach asks players to run from one corner to the other corner diagonally across What is this distance Round your answer to the nearest tenth 4 points

For problems 3 and 4 find the missing side of the triangle Leave answers in simplest radical form 2 points each 3 8 12 4 17cm 8cm

D 18 5 If AABC AEFG and the mzB 8x 4 mC 3x 9 mzG 9x 9 what is the m E