Explore BrainMass
Share

Triangles

Saccheri quadrilaterals; Lambert quadrilaterals

Draw a diagram of a Saccheri quadrilateral ABDC, where (a) A and B are a pair of consecutive vertices (b) sides AD and BC are a pair of opposite sides (c) angles A and B are right angles (d) sides AD and BC are congruent. Then let M be the midpoint of AB, and drop a perpendicular from M to CD with foot N. Once

Geometry Problems

Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. The Pythagorean Theorem states that the square of

Geometry : Right Triangle Inscribed in a Circle

Using the diagram attached: 11. What is the measure of arc AC? 12. If ABC is a 30-60-90 triangle, with angle ACB at 30 degrees, and line segment AC is the diameter of the circle, then if the length of line segment AB is 4, what is the radius of the circle? 13. Working with the information from 12 from here to #16, what is

Arcs and chords of a circle.

Using the diagram at right: 1. If the diameter of circle M is 20, and the length of line segment DF is 12, what is the length of segment MJ? 2. If the measure of arc BFE is 80 degrees, then what is the measure of angle BME? 3. If there were an imaginary angle ACB, what would the measure of that angle be? (Hint: Remember that

Solutions to problems in geometry

See attached file for full problem description. 1. Use the figure below to find the following: 2. a) Find the complementary angle of 26 b) DEF and GHI are supplementary angles and GHI is fourteen times as large as DEF. Determine the measure of each angle

Area of an isosceles triangle and volume of a prism.

If I have a right prism with the prism height being 8 and the prism base being an isosceles triangle with a base of 3 (sides of 6) what is the lateral area and the volume of the prism, also what is the triangle's height by using the Pythagorean theorem?

Find the area covered by the chemical retardant.

1) In mountain communities, helicopters drop chemical retardants over areas which approximate the shape of an isosceles triangle having a vertex angle of 38 degrees. The angle is included by two sides, each measuring 20 ft. Find the area covered by the chemical retardant. 2) The chemical retardants are freight shipped from

Geometry : Hexagon and Football

1. Show the necessary steps for finding the length of each side of a regular hexagon if opposite sides from midpoint to midpoint are 18 inches apart. 2. Without cutting or destroying a football, how would you find the area and volume of a football. Include any necessary formulas and measurements to implement your idea.

Triangle Word Problem Using Bearings

A surveyor finds that a tree on the opposite bank of a river has a bearing of N 22 degrees 30'E from a certain point and a bearing of N 15 degrees W from a point 400 feet downstream. Find the width of the river.

Right Triangle

1. Find the length L from point A to the top of the pole. 2. Lookout station A is 15 km west of station B. The bearing from A to a fire directly south of B is S 37°50' E. How far is the fire from B? 3. The wheels of a car have a 24-in. diameter. When the car is being driven so that the wheels make 10 revolutions per seco

A Little League team is building a backstop for its practice field

A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high. All sides of the backstop including base and the center pole are to be made of aluminum tubing. How many feet of

Geometry has many practical applications in everyday life

See attached file for full problem description. Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations

Proof involving equilateral triangle

I need to see a construction and proof. Let (triangle DEF) be equilateral triangle and Q is a point inside. Prove that the sum of the three distances from Q to each side is equal to the altitude DD'.

Writing Functions from Word Problems

20. A wire 10 meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle. a. Express the total area A enclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle. b. What is the domain of A? c. Grap

Geometry Applications Word Problems

Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. The Pythagorean Theorem states that the square of

Solving Radical Equations and Finding Side of a Cube Given Volume

1) Solve the following equations. a) sqrt(x) - 1 = 4 b) sqrt(x^3) = 8 c) third root of x^2 = 4 2) Is sqrt(x^2) an identity (true for all values of x)? Answer: Explain your answer in this space. 3) For the equation x - sqrt(x) = 0, perform the following: a) Solve for all values of x that satisfies the equatio

Explain matrices and triangles

Researchers at the National Interagency Fire Center in Boise, Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States. In an effort to dispatch firefighters for containment, scientists and meteorologists attempt to forecast the direction of the fires. Some of this data can be

Find the Hypotenuse

1. A right triangle is a triangle with one angle measuring 90 degree. In a right triangle the sides are related by Pythagorean Theorem, c^2=a^2+b2 where c is the hypotenuse (the side opposite the 90 degree angle). Find the hypotenuse when the other 2 sides measurements are 3 feet and 4 feet.

Triangle construction....

1. Show how to construct a triangle given the length of one side, the distance from an adjacent vertex to the incenter and the radius of the incircle. 2. Show how to construct a triangle ABC given the length of side BC and the altitudes from B and C

Constructions of Triangles for Midpoints

1. Show how to constract a triangle given the 3 midpoints of its side. 2. Show how to construct a triangle given the lenght of one side, the size of an adjacent angle and the lenght of the median from that angle.

Diagonals of Quadrilaterals

1- prove that the diagonals of a rhombus bisect each other at right angels. 2- prove that diagonals of a kite or dart (possibly extended) intersect at right angels. (Note: kite is a convex quadrilateral in which 2 pairs of adjacent sides are congruent dart is a non convex quadrilateral in which 2 pairs of adjacent sides are

Open-Jaw Inequality

Prove the first half of the open-jaw inequality where the point G lies inside triangle DEF i.e. show that if x less than y => AC < DF. Please see the attached file for the fully formatted problems.

Right Triangles

A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, , where c is the hypotenuse (the side opposite the 90° angle). How do I find the hypotenuse when the other 2 sides' measurements are 6 feet and 8 feet.

Geometry Proofs : Triangles, Bisectors and Midpoints

1- Given triangle as shown (infigure 241W) with AF = 1/4 AB, AE = 1/3 and BE Intersect CF = O (BE has ray bar on top and CF has distance bar on top) prove that AO hits BC At its midpoint. 2- Use Ceva's theorem to prove that the internal bisectors of the angles of a triangle are concurrent (cevas theorem: given triangle AB

Internal bisectors and incenter of a triangle

1- Given triangle ABC, prove that an internal bisectors of an angle of a triangle divides the opposite sides (internally) into two segments proportional to the adjacent sides of the triangle. That is prove that DB/DC = AB/AC. (D is the point where e internal bisector of <A meets with BC) 2- Given triangle ABC with in-center