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# Triangles

### Prove the Theorem of the Broken Chord

The theory of the broken chord asserts that if AB and BC make up a broken chord in a circle, where BC > AB and if M is the midpoint of arc ABC, the foot F of the perpendicular from M on BC is the midpoint of the broken chord ABC.

### Percent of the Rectangular Prism Outside of the Triangular Prism

AEF is a triangle , ABCD is a rectangle AB = 6 AE= 10 AD = 11 EF = 5 AF = 5 sq.rt. 5 The attached picture is the base of a right prism - a triangular prism inside of a rectangular prism. Both prisms are 20 in height. What percent of the rectangular prism is outside of the triangular prism.

### Sides of a Triangle are all Diameters of Semicircles : Area of Shaded Region?

Triangle ABC is a right triangle in a semicircle with AC as a diameter. Semicircles are also drawn with legs AB and BC as diameters. If AB=12 and BC = 5, What is the sum of the shaded areas? Please see the attached diagram.

### Equations of Lines and Intersections

The diagram below (see attachment) shows a triangle ABC whose vertices are at A (-1, 3), B (6, 5) and C (8, -3). The line BP is perpendicular to the line AC, and M is the midpoint of BC. Note that BP is called an altitude of triangle ABC and that AM is called a median of triangle ABC. a) Find the gradient of i) The

### Ratio of the Area of Two Triangles

Two sides of triangle RST are 6 and 10. Find the ratio of the area of triangle RSH to the area of triangle RHT if RH bisects angle SRT.

### Find Volume of the Solid from Revolution of a Right Triangle

A right triangle with legs of 5 and 12 is rotated about it's hypotenuse to form a solid which is pointed at two ends. What is the volume of that solid? (Exactly in terms of pi).

### Rectangle Area of Midpoints

How do I go about finding the area of triangle ACE in the following: In rectangle ABDF the following is given: AB=24 BC=7 AF=16 E is the midpoint of FD

### Geometry : Volume of Cubes and Area of Triangle

A large cube is 2 feet on each edge. How many cubes - one inch on each edge- will it take to fill the large cube? If the base of a triangle is increased by 20% and the altitude to that base is decreased by 40% then by what percent is the area changed? Is that an increase or a decrease? Decrease by 30%. Is this correct?

### Find values of p for which the faces of a planar p-regular graph are all triangles.

The faces of a planar p-regular graph are all triangles (that is each face has degree three). Determine, with proof, the values of p for which this is possible. (Remember a p-regular graph has all vertices of degree p).

### Equilateral Triangles within a Closed Area

(a) Figure 1 shows a closed area ABCDEF in which ABDE is a rectangle and BCD and AFE are equilateral triangles. AE x cm and AB y cm. (i) Find, in terms of x andy, a formula for the area enclosed by the figure ABCDEF and a formula for the perimeter ABCDEF. (ii) Find the minimum perimeter (to two decimal places) of ABCDEF enclos

### Acute Angles and Right Triangles

Find the exact value of each [side] labeled with a letter {see attachment for diagram}

### Solve for beta

In the attached problem, I am trying to solve for Beta. We have done other problems that solve for the faces of the triangle but not sure on how to solve for this face.

### Degree of Angles in Triangles

1) For the given triangles, a = 14.5m, b = 6.03m and alpha = 55.6 degrees. Find theta. Answer in units of degrees. No picture, but use points (0,0), (5,0), (5,7) for triangle one. The x side is labeld a and the angle near the origin is alpha. Now the second triangle is against the y side or against the side from (5,0)

### Right Triangle Functions

Please give answer and explanation and or steps if needed please to check my work. 1) Draw a right triangle whose sides (not the hypotenuse) have lengths of 8 and 15. Angle A is adjacent to the side of 8, and angle B is adjacent to the side with the length of 15. The tan A=? 2) For the same triangle in question 1 do f

### Perimeter of a Triangle

The length of the sides of a triangle are 1/x, 1/2x, and 2/3x meters. Find a rational expression for the perimeter of the triangle (your final expression must contain only one term). Use Appendix A of Dugopolski for formulas of Geometric shapes. (Question also in attachment).

### Geometry Construction- To Construct A Congruent Triangle

Step 1. Draw an acute scalene triangle. Label the vertices A, B,C on the interior of each angle. Step 2. Construct a segment congruent to line segment AC. Label the endpoints D and E. Step3. Adjust the compass setting to the length of line segment AB. Place the compass at point D and draw a large arc above line segment D

### Geometric Construction : Construct A Median Of A Triangle

Step 1. Draw a scalene triangle and label the vertices, A,B,AND C. Step 2. The side opposite vertex A is line segment BC. Find the midpoint of line segmentBC by constructing the bisector of line segmrnt BC. label the midpoint M. Step 3. Use a straightedge to draw linesegment AM. Line segment AM is the median of triang

### Create Construction : Triangles, Arcs and Line Segments

Please create this construction where I can see it. You may have to use a dark marker. Also, make the drawing large. Thank you. Step 1. Draw a scalene triangle and label the vertices ,A,B and C. Step 2. Place the compass at point B and draw an arc that intersect line segment AC in two points. Label the points of inters

### Simple Geometry : Constructing a Golden Triangle

Given a line segment of length 1 inch, how do I construct a line segment of squareroot(6), squareroot(7), squareroot(8), etc. Also, given a wire of total length 4236 feet, how do I construct a golden triangle from the wire?

### Finding a Distance (X) : Triangles and Circles

In the problem I am being asked to solve for the value of X. I have tried setting up right triangles and a mix of right and oblique triangles but have not been able to get the right combination. The value of A is 3.5 and the answer of X is 1.8376. The book gives the answer and we construct the problem.

### Finding a Distance (X) : Triangles and Circles

I would like help in setting up the construction to solve for the value of X in this problem. I have tried to form right triangles to solve it but not been able. The value of Theta is 52 degrees and the value of X the book gives is 1.1763. Please see the attached diagram.

### Finding Distance from a Diagram Containing Triangles and Circles

I have tried setting up this problem using right triangles but have not been able to solve it correctly. This problem is not as simple as it looks. It cannot be assumed that the bottom of the circle is tangent to a line drawn across the bottom. Solving for that one triangle is part of the solution. Theta is given as 20 degree

### Sine Rule in Triangles

Q: I know the length of two sides of a triangle. I know the degree of the hypotenuse. How do I figure out the length of the base. Example: The length of two sides is 144 inches. The angle is 22.5%. How long is the base?

### Plane Separation : Convex Triangle

If A,B,C are noncollinear in a metric geometry prove that triangle ABC is convex.

The perimeter of a building is 74'by 59'by 103'by 121'. How can the square footage of the building be calculated?

### Centroid is the Balance Point of a Triangle

Need to prove that the centroid is the balance point of a triangle using only GEOMETRY with no vector addition allowed and I can't use the "equal areas" argument as far as the 6 triangles that are made with the medians. Thanks much

### Setting Up Right Triangles

I would like to get some help setting up the right triangles so that I can solve this problem. The dimension of A is 4.75. Please see the attached file for full problem description.

### Area of Parallelogram

1. Find the area of parallelogram ABCD, given that AB = BE = ED = 1, and angle ABE = 90 degrees. See attached file for full problem description.

### Value of Triangle Functions

I would like to get assistance in setting up the attached problem so that I can solve it. The value of A is 3.65 and the book gives the answer as 2.2748. thank You

### Solve for X from a Diagram: Setting Up Triangles

I would like assistance in setting up the attached problem in order to solve it. A=2.875. X is the value that needs to be solved. In the book they give the value of X as 2.1091. See the attached file.