2D Geometry Questions and Answers

The shadow of a vertical tower is 78.0 ft long when the angle of elevation of the sun is 33.0°. Find the height of the tower. The tower is___ft tall. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.)

The area of a circle is 25mcm². What is the circumference of the circle? Write you answer as exact.

The sum of the interior angles of a convex polygon is 2520°. Determine how many sides the polygon has.

The equation D=1/2 n(n-3)gives the number of diagonals D for a polygon with no sides. Find the number of sides for polygon that has 152 diagonals.

Suppose that the measure of an interior angle of a regular polygon is 157.5". How many sides does that polygon have? # of Sides =

What is the measure of EACH exterior angle of the following polygons? a) Square > Exterior Angle = b) Regular Hexagon -> Exterior Angle = c) Regular Octagon --> Exterior Angle = d) Regular 12-gon- --> Exterior Angle =

What is the sum of the measures of the exterior angles of a polygon with 12 sides?

Find the lateral surface area and total surface area of the cube with side length s = 4.2 mm. Round to the nearest whole number, if necessary. LSA = TSA =

If W(-10, 4), X(-3, -1), and Y(-5, 11) classify AWXY by its sides. Show all work to justify your answer. Classify: WX = XY = WY=

Sketch the graph of: y=5cot (3x+ π/2) y = 3sec (1/4x - π/6)

A parallelogram is a four-sided figure whose opposite sides are parallel and equal in length. Alex is drawing parallelogram ABCD on a coordinate plane. The parallelogram has the coordinates A(4,2), B(0,-2), and D(8,-1). Which of the following coordinates should Alex use for point C? A (6,-3) B (4,-5) C (10,-3) D (4,3)

Sketch the graph of the function y = 2csc(2x-π/2) over one period. Please label at least 2 key points and show and label any vertical asymptotes on your graph.

Select the graph of the transformation of f(x)=3x Give the horizontal asymptote, the domain, and the range. f(x) = 3x - 2

Can two points on a line be on a parabola? Proceed by contradiction

Given the equation of f(x)=1/4 (x-3)² - 6 list the EXACT VALUES of any invariant points for y = √f(x)

Convert, 2x+7y=-3, from rectangular to polar form

Consider a triangle ABC with the features c=65 meters and m∠B= 23. Find the values of side length b for which there would be zero, one, or two possible triangles for this situation. a) For what values of b would there be ZERO possible triangles? b) For what values of b would there be ONE possible triangle? c) For what values of b would there be TWO possible triangles?

Find the radius of a circle with a diameter of 38 cm.

Graph the parabola. y=-3x² +24x-44

In ΔABC, LC is a right angle and m∠A = 40°. Which list shows the sides in order from longest to shortest? AB, BC, AC BC, AB, AC AC, BC, AB AB, AC, BC

A triangle has sides with lengths of 12 feet, 12 feet, and 16 feet. Is it a right triangle? yes no

A rhombus has diagonals of 5 and 7. Find the length of its sides.

Given: Rectangle ABCD Prove: AC=BD

If the perimeter of a rectangle is 30 cm and the area is 50 square cm, then what are the dimensions of the rectangle? The width, or shorter side is _______cm The length, or longer side is ________cm

Given that the area of an equilateral triangle is 331 cm², find its perimeter. The perimeter of the triangle is Give your answer to 2 decimal places.

Write 2/7 as a decimal rounded to the nearest tenth.

Write 2.012 as a mixed number and as an improper fraction. Write your answers in simplest form.

Write 1.15 as a mixed number and as an improper fraction. Write your answers in simplest form.

(a) An angle measures 51°. What is the measure of its supplement? (b) An angle measures 33°. What is the measure of its complement?

(a) 43.7 is what percent of 9.2? (b) What is 55% of 19.6?

A pail holds 2 3/4 gallons of water. How much is this in cups? Write your answer as a whole number or a mixed number in simplest form. I

Write 67/11 as a decimal rounded to the nearest hundredth.

Find the least common denominator (LCD) of and 4/15 and 9/10.

A rirg shaped region is shown below. Its inner diameter is 38 m, and its outer diameter is 50 m. Find the area of the shaded region. Do not round any intermediate steps. Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas.

The circumference of a circular garden is 138 feet. What is the radius of the garden? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas.

The circumference of a circular field is 310 yards. What is the radius of the field? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas.

A ring-shaped region is shown below. Its inner radius is 7 cm, and its outer radius is 10 cm. Find the area of the shaded region. Do not round any intermediate steps. Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas.

What is the y-intercept of the line that has a slope of -4 and passes through the point (4, -6)? (A)-10 (B)-6 (C)8 (D) 10

Determine the equation of the circle that is centered at (0, 0) and passes through the point (3,-7).

The size of a laptop is determined by the diagonal of its screen. If a 11- inch laptop has a screen that is 7.3 inches tall, how wide is the screen? The screen is __ inches wide.

The center of a circle of radius 3 in. is at a distance of 50 in. from the center of a circle of radius 27 in. There are two circles that do not touch, four segments, and five labeled points. What is the exact length (in inches) of common internal tangent AB? (Hint: Use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.) in

Three of the four angle measures in a quadrilateral are 90, 90, and 125. Find the measure of the fourth angle.

If two sides of a triangle have the following measures, find the range of possible measures for the third side. 12, 8 5, 16 2,7 44, 38 21, 22 81, 100

If two triangles are congruent, which of the following statements must be true? Check all that apply. A. The corresponding sides of the triangles are congruent. B. The triangles have the same shape. C. The triangles have the same size. D. The corresponding angles of the triangles are congruent.

1. Parallel Line Construction: For this part of the assignment you will construct a parallel line through a given line and point. First, draw a segment (AB) and point C on your paper. Next, construct a line through point C that is parallel to AB. Label all points and lines used in the construction. 2. Perpendicular Line Construction: For this part of the assignment you will construct a perpendicular line to a given segment that passes through a given point. First, draw a segment (AB) on your paper. Draw a point (C) above that line. Construct a perpendicular line through segment AB and point C. Label all points. and lines used in the construction.

The vertices of the transformed figure are L' (0, 15), M (-15, -15), and N' (18, -6), and the original figure are L (0, 5), M (-5, -5), and N (6, -2). Find the scale factor used in this transformation. 3 2 5 -3

Find the scale factor, if the point A (2, 6) is dilated to A' (8, 24). 4 1/4 2 1/2

What is the perimeter of the ellipse defined by the equation: 36x^2 + 4y^2 = 144?

Consider the following planes. x+y+z= 9, x + 3y + 3z = 9 (a) Find parametric equations for the line of intersection of the planes. (Use the parameter t.) (x(t), y(t), z(t)= (b) Find the angle, in degrees rounded to one decimal place, between the planes.

Select the correct answer. The vertices of a hyperbola are at (-5, -2) and (-5, 12), and the point (-5, 30) is one of its foci. What is the equation of this hyperbola? A. (y-5)^2 /24^2 - (x+5)^2 / 7^2 =1 B. (x+5)^2 /24^2 - (y-5)^2 / 7^2 =1 C. (x+5)^2 /7^2 - (y-5)^2 / 24^2 =1 D. (y-5)^2 /7^2 - (x+5)^2 / 24^2 =1