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# Triangles

### Finding Length of the Side of a Triangle

Given a=41degrees, B=101degrees, and a=30.1, approximate the length of side b in a triangle ABC. Given a=100degrees, B=30degrees, and c=110.3, approximate the length of side b in a triangle ABC.

### Geometry : Triangle in a Cone

In the diagram attached, I have to show that: curly r-bar = sqrt(h^2 + curly-r squared - sqrt(2).h.curly-r). So far, I've only been able to come up with the obvious fact that: curly - r^2 = sqrt(h^2+h^2) = sqrt(2).h

### Geometry : Parallelograms and Isosceles Triangles

Use the given coordinates to find the coordinates of point Q. Please see the attached file for the fully formatted problems.

### Geometry : Medians of Triangle Proof

O is the intersection point of the medians of a triangle ABC. The medians are AD, BE, CF. what is the ratio of the area of triangle EOC to triangle ABC?

### 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&#61616; b) &#61648;DEF and &#61648;GHI are supplementary angles and &#61648;GHI is fourteen times as large as &#61648;DEF. Determine the measure of each angle

### Geometry : Polygons, Real-Life Applications of Right Triangles, Volume of a Pill Capsule

1. What is a polygon? What is the difference between an equiangular polygon, an equilateral polygon, and a regular polygon? Provide an example of each. 2. We can use the Pythagorean Theorem to solve problems that involve right triangles. Provide an example of a day-to-day situation that involves right triangles and the use of t

### Solving for Geometry Word Problems

a. A certain wheel has a diameter of 98 inches. If that wheel travels for 108 revolutions, then. Questions: How many years has it gone? (use 22/7 for pi) b. A regular hexagon and an equilateral triangle are equal in area. The perimeter of the triangle is 36. Question: How long is one side of the hexagon? c. The base of

### Area and Perimeter of Triangles

28. Find the area and perimeter of an equilateral triangle whose altitude measures 6 cm. 29. If the area of an equilateral triangle is 100 sq cm, find the length of a side.

### High School Geometry Problems

Please see the attached file for the fully formatted problems. Given: <D and <C are right angles (triangle APR) = (triangle BQT) Prove: (triangle ADF) = (triangle BCE)

### Geometry: Congruent Triangles

Given: The triangle ABC is an equilateral triangle and the angle 1 = the angle 2 = the angle 3. Prove: The triangle AFC, the triangle CEB and the triangle BDA are all congruent.

### 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?

### Geometry Proof : Isosceles Triangle and Bisector

ABC is an isosceles triangle. M is the midpoint of side BC. E is a point on AC. The (angle) bisector of angle ABE intersects AM at F. What is EF? Prove your Conjecture.

### 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

### Finding the Side of a Scalene Triangle

I have a scalene triangle. One side is 241 long, the other is 232 feet. I need to know what the third side would be.

### Geometry : Construction and Conjecture - What kind of quadrilateral is ACBD?

J and k are parallel lines. Line d intersect j and k respectively at A and B. Points C and D are equidistant from j, k, and d. What kind of quadrilateral is ACBD? Prove your conjecture.

### Geometry Proofs Involving Triangles

Geometry Problems: Solve the proofs in question 7 and question 8. Number 7: We are given that AE = DB, FG = CG, and angle FGE = angle CGD, and we want to prove that angle A = angle B. (Note: AE = DB not AE = BE.) Number 8: We are given that DB bisects angle ADC and angle 3 = angle 4, and we want to prove tha

### 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.

### Solving Triangles

Find all possible solutions for triangle ABC if A=55 degrees, a=12, and c=13.

### 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.

### Solving Triangles : Law of Sines

Use the law of sines to solve the triangle. If two solutions exist find both. A = 110 degrees, a= 125, b= 200

### 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

### Conversion from radians to degrees.

Convert 4.752 radians to degree measure. Round to three significant digits.

### Finding the Hypotenuse of a Right-Triangle

Find the third side, c, of the right triangle where a=87.5ft and b=192 ft

### Solve the following five geometry problems

The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, as shown in the diagram attached. See attached file for full problem description. Solve the following problems in a Word document. 1. A Little League team is building a backstop f

### 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

### Surface Area Word Problem

A water tank has the shape of a cone. The tank is 10m high and has a radius of 3m at the top. If the water is 5m deep (in the middle) what is the surface area of the top of the water?

### Triangle Inequality Theorem

Write a compound inequality to describe tha range of possible measures for side c in terms of a and b. Assume that a > b > c.