Geometry Questions

K Use the given figure to find the measures of the numbered angles given that lines m and n are parallel The measure of angle 7 is 60 The measure of angle 9 is 9 6 7 10 2 60 4 3 5 64 8 11 12 m n

3 Use the given figure to find the measures of the numbered angles given that lines m and n are parallel The measure of angle 7 is 60 6 7 910 2 4 64 8 11 12 m n

Solve the following equation for x in radians in the interval 0 2 sin x 1 2 Give the exact value radian angle measures when possible If needed give the approximate value to the nearest 2 decimal places You may select more than one answer

A toy rocket is shot vertically into the air from a 72 foot tall launching pad with an initial velocity of feet per second Suppose the height of the rocket in feet t seconds after being launched can be modeled by the function where is the initial velocity of the rocket and is the initial height of the rocket How long will it take for the rocket to reach its maximum height What is the maximum height

A group G of six matrices is generated by A 11 and B 3 under matri multiplication modulo 2 List the six matrices in G if G is isomorphic to S3

Use the power reducing formulas to rewrite sin 5x cos 5x in terms of the first power of cosine Simplify your answer as much as possible To indicate your answer first choose one of the four forms below Then fill in the blanks with the appropriate numbers OnSx cos Sx cos k cos sin 5x cos 5x coi cos O O sun 5x cos 5x cox sin 3x cos3x cos ow Transcribed Text TICKOM 2 sin u Power reducing formulas COS U S 2 tan u 1 cos2u 2 1 cos2u 2 1 cos2u 1 cos2u X 1 cos21 S

Assume Za is opposite side a LB is opposite side b and 4y is opposite side c Solve triangle ABC if ZA a 40 8 b 12 1 km and c 17 3 km Using the Law of Cosines a km Your answer should accurate to 2 decimal places Using the Law of Cosines again cos B cos Your answer should accurate to 5 decimal places Thus Your answer should accurate to 2 decimal places cos C cos y Your answer should accurate to 5 decimal places Thus y Your answer should accurate to 2 decimal places

If 0 x 2 find all values of x that satisfy the following equation Select the correct answer below O x 4 and 5 x 5T and 75 O O O X X 5 7 19 18 18 18 4 5 10x 999 117 16 17 9 2 9 29 cos 3x 3 2

olve each equation x in radians and theta in degrees for all exact solutions where appropriate Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth Write answers using the least possible nonnegative angle measures tan x tan x 2 5

If 0 x 2 find all values of x that satisfy the equation Select the correct answer below O x 3 x 3 and S X 3 and 4 tan x 1 sec x 2

We can use the Law of Sines to find the two missing angles Select sin B sin 22 sin C sin 0 78 51 3 14 2 sin 22 10 9 22 7 sin 22 10 9 sin 0 488 29 2 B Select 0 78 0 488 The problem with those two angles is Select Find the Missing Angles Select Since Select is the longest side it must be opposite the largest angle which must mean B is an obtuse angle with a reference angle of 51 3 sin B and C 29 2

If B is an obtuse angle then in standard position it s in quadrant 2 and has the same from the previous triangle B Select C Select C Select ngle reference angle as the acute B Using the Law of Sines again gives us c for this triangle

In this example h a b so there are two triangles a triangle where B is acute 1 and a triangle where B is obtuse 2 35 b 20 C 2 We know a 15 We need to find c C and B for each triangle Acute B Triangle a b 15 sin A sin B sin 35 Solving this equation tells us that B Select 1 a 15 SO 20 sin B All of the angles of any triangle sum to 180 so C Select We can use the Law of Sines again to find c If we plug the C b values we found into sin C sin B calculate c then we can

Plot the point whose polar coordinates are given Then find the Cartesian coordinates of the point a 6 47 x y 3 t x y c 5 x y

A curve is defined by the parametric equations x t 2cos t 2 and y t 4sin t Draw this graph by using the draggable points

0 r 3 2 plane co TU y 4 2 sting of points whose polar coordinates satisfy the given conditions 2 2 X 4 2 y 4 4 4 2 y 2

Consider a four year project with the following information initial fixed asset investment 500 000 straight line depreciation to zero over the four year life zero salvage value price 35 variable costs 26 fixed costs 200 000 quantity sold 80 000 units tax rate 25 percent How sensitive is OCF to changes in quantity sold Do not round intermediate calculations and round your answer to 2 decimal places e g 32 16

A 120 ft height post casts a shadow that is 150 ft long What is the angle of elevation of the sun O 30 O 38 6 O 25 O 15

The angle of elevation of a man standing on a road to the top of a building is 60 degrees If the height of the building is 30 feet find the distance between the man and the base of the building O 60 feet O 30 feet O 17 32 feet O 12 98 feet

Question 7 Points 2 A man walked 5 miles right and read a sign that said 20 miles north to Atlanta How far is Atlanta from the starting point O 5 miles O 20 miles 20 62 miles O 25 miles

What is the formula for cos 0 O Cos 0 Opposite Cos Hypotenuse O Cos 0 Adjacent Hypotenuse Cos 0 Adjacent Opposite Hypotenuse Opposite

Question 3 Points 3 The angle of elevation of the top of a hill from its foot is 30 If the height of the hill is 200 m what is the distance of the center of the hill from its foot O 346 62 m O 116 47 m O 11 47 m 15 47 m

Question 4 Points 3 The length of a rectangular painting is 7 inches longer than its width If the diagonal is 13 inches what are the dimensions of the painting O 5 inches by 11 inches O 5 inches by 12 inches O 5 inches by 13 inches O 11 inches by 12 inches

Question Points 2 Maggie ran 3 miles east and then 4 miles north How far is she from her starting point 3 miles 4 miles O 5 miles O 7 miles

Question 5 The angle of elevation of a car on a road to the top of a tower is 45 If the distance between the car and the tower along the road is 22 ft find the height of the tower O22 ft O 45 ft Points 1 O 67 ft O 180 ft

Question 2 The dimensions of a room are 45 ft by 40 ft respectively Find the length across the diagonal of the room to the nearest whole number O 60 ft 40 ft O 20 ft Points 2 O 10 ft

Question 6 Find the length of AB 3 in Points 3 C 4 in O 5 inches 6 in O 10 inches 8 in B

Question 10 Points 2 C and D are complementary angles Which of the following measures cannot be true Om C 30 and m D 60 mzC 60 and m D 30 O m C 65 and m D 35 O m C 55 and m D 35

Question 8 Points 2 Express sin 850 in terms of cos O cos 35 Ocos 25 O cos 15 O cos 5

Write cos 5 in terms of sine O sin 10 O cos 15 O sin 5 O sin 85

Question 7 Points 1 The given angles are complementary Find the missing angle from the given figure P K O 35 O 53 O 37 73 37 R PL

Identify the name of the following pair of angles 70 O Straight angles O Obtuse angles 20 O Complementary angles

Find the value of sin 15 cos 75 1 O 1 O 0

Which of the following is equal to one O O cos 30 sin 60 cos 45 sin 60 cos 30 sin 45 O cos 45 sin 55

Question 6 If sin x 0 8 then what is the value of cos 90 x 0 2 0 4 O 0 6 Points 1 O 0 8

Simplify sec 900 8 cot 90 0 O csc tan 0 O sec 0 cot 0 O cos 0 sin 0 O sin 0 cos 0

Find the missing angle from the given figure 25 O 55 65 O 85 O 45

5 For the functions f x x 1 and g x x 5 fog x A x 4 x 25 x 26 D x 10x B C 25 E x 10x 26

Suppose that 3x 2y t and x t cos 0 Find at ax t and at ax y

Graph the image of the figure using th 1 reflection across the x axis K W

Find the minimum height h above the surface of Earth so that a pilot at point A in the figure can see an object on the horizon at C 145 mi away Assume 4 00 x 10 mi as the radius of Earth OCCES The minimum height is about mi Do not round until the final answer Then round to the nearest hundredth as needed 145 mi

9 1 9 3 Simplify these expressions 1 sec B cot B cot B cos B 2 csc B tan B tan B sin B 3 3 sin 2 x 1 cot 2 x 4 5 cos 2 x 1 tan 2 x 5 4 cos B tan B sin B 6 6 sin B cot B cos B

Geometry problems often require proving triangles are congruent Match the reason with the best pictorial representation A B A B C D A B 8 E D Choose AAS SSS HL ASA SAS Choose Choose Choose

The quadrilaterals ABCD and JKLM are similar Find the length x of JK C X B D X 14 8 S M

The pentagons JKL MN and PQRST are similar Find the length x of PQ X M 1 L 0 3 N K 2 S 0 6 R 2 4 1 8 T Q 0 6 P

b 0 A miles a B Two radar stations 6 miles apart are tracking an approaching airplane The angle of elevation from stations A and B to the plane is 61 and 27 respectively Calculate the distance between the airpla and stations A and B respectively Give your answer in miles and to two decimal places miles

Define the following To cut into two equal sections A numbering system used when measuring angles How far apart two points are from each other The ratio of a circle s circumference to its diameter Choose Choose Choose Choose

Define the following A figure resembling a stretched circle Part of a line using two points and all of the points between them The location half way between two point A curved figure resembling a valley Part of a line with a starting point and all of the Choose Choose Choose Choose Choose

From the following picture match the pairs of angles to the correct description of the angle relationship 2 7 1 8 5 8 3 7 1 2 3 5 6 7 8 Choose Choose Corresponding Angles Consecutive or Same Side Interior Angles Alternate Exterior Angles Vertical Angles

Match the following A triangle in which 2 sides have the same length A triangle in which all of the angles have the same measure A triangle in which one angle has a measure of 90 degrees A triangle in which all sides have the same length A triangle in which the 3 sides have Choose Choose Choose Choose Choose