2D Geometry Questions and Answers

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

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

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

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

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 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

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

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 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

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

7 If ZA 48 ZB 72 ZC 60 and the measures of the arcs are as indicated in the following figure find the measures of EF GH and DI A 100 D I B ENF 110 60 G H C

The figure shows a 700 foot tower on the side of a hill that forms a 7 angle with the horizontal Find the length of each of the two guy wires that are anchored 80 feet uphill and downhill from the tower s base and extend to the top of the tower how Transcribed Text 700 feet 80 feet J AIKAIPANNE TAKELT C 80 feet

A tank contains 9 000 L of brine with 19 kg of dissolved salt Pure water enters the tank at a rate of 90 L min The solution is kept thoroughly mixed and drair From the tank at the same rate a How much salt is in the tank after t minutes kg y b How much salt is in the tank after 30 minutes Round your answer to one decimal place y kg

Sure arc 1 are 2 4 Find the measure of arc 1 round to one decimal place degrees wing two questions arc 2 5 Find the measure of arc 2 round to one decimal place degrees

Use the diagram for the following two questions 4x 3 6 Find the measure the arc degrees arc 7 Find the measure of the angle angle degrees

8 Find angle x round to one decimal place degrees

x 1 12 a N 2 7 x 1 b x 1 3 5 x 2

3 a 15 24 b 2 ft 2 yd 1 yd 3 ft c 2 m 150 cm 1 m 100 cm d 2 m 1 lb

5 Sarah ran the 300 m hurdles in 47 7 seconds In meters per second find the rate at which Sarah ran Give the answer to the nearest tenth of a meter per second

36 If the ratio of the measure of the complement of an angle the measure of its supplement is 1 4 find the measure of t angle

14 a x 1 X X x 1 b x 2 X 2x x 2

In Exercises 5 to 14 find the value of x in each proportion 7 21 24 5 a X 4 9 12 b X

Identify the type and number of local extrema 8 6 80 60 40 20 20 40 60 80 y 2 4 6 8 X

es 153846 assignments 12018853 Write an equation for the line containing the point 1 3 and parallel to the line y x 6 9 10 perpendicular to the line y x 6 Write an equation for the line containing the point 5 3 and 11 parallel to the line y 4

Write an equation for the line containing the point 2 3 and parallel to the line y 2x 3

Use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem PV 15 000 i 0 01 PMT 550 n n Round up to the nearest integer

ind the unknown angles in triangle ABC for the following triangle if it exists C 45 20 b 25 4 m c 361 m Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA There is only one possible set of remaining angles The measurements for the remaining angles are A Do not round until the final answers Then round to the nearest whole number as needed OB There are two possible sets of remaining angles The measurements for when B is larger are A and B O not round until the final answers Then round to the nearest whole number as needed OC No such trange exists and B and B The measurements for when B is smaller are

Suppose functions f x and g x are defined as follows x 1 2 3 f x g x 3 2 1 4 2 1 4 3 4 5 5 That is f 1 3 g 1 2 f 2 1 g 2 1 and so on Evaluate each of the following expressions ff 1 fog 2 gof 3 gog 4 5

An engineer designs a satelite dish with a parabolic cross section The dish is 18 ft wide at the opening and the focus is placed 9 ft from the verlex a Position a coordinate system with the origin at the vertex and the x axis on the parabola s axis of symmetry and find an equation of the parabola b Find the depth of the satellite dish at the vertex a The equation for the parabola is Type an equation Simplify your answer 180 G The figure may not be drawn to sca

10 If G is the midpoint of FH FG 14x 25 and GH 73 2x find