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# Triangles

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### Geometry - Construct an Altitude in an Equilateral Triangle

Construct an equilateral triangle. Then construct one of its altitudes. If the sides each have length 1, how long is the altitude?

### Prove triangle ABC is congruent to triangle DBE.

1. Write a proof. AB*BE = CB*BD. Prove triangle ABC is congruent to triangle DBE. 2. A parent group wants to double the area of a playground. The measurements of the playground are width is 2W and the length is 2L. They ask you to comment. What would you say? 3. Find the length of the altitude drawn to the hypotenuse.

### Geometry Theorem Proof

Prove that an interior angle bisector of any triangle divides the side of the triangle opposite the angle into segments proportional to the adjacent sides.

### Solution of Triangles

Solve the triangle in which a = 36, b=24, B= 25 Degrees (This is an ambiguous case).

### Geometry - Parallelograms and Triangles

Please solve. See the attached file for diagrams. Question 1 The preferred seating area at the Music Theatre is the shape of a parallelogram. Its base is 34 yd and its height is 39.6 yd. Find the area. Question 2 The diagonal of a small pasture measures square root 12,617 feet in length. Find the le

### Introduction to Lobachevski's Geometry

Write a brief description of Lobachevsky's geometry.

### Triangle Measures Angles

Solve. A triangle has three angles, R, S, and T. Angle T is 40Â° greater than angle S. Angle R is 8 times angle S. What is the measure of each angle?

### Congruent Circles in an Equilateral Triangle

3 congruent circles with radius 5 are tangent to each other. The circles are enclosed in an equilateral triangle. What it the perimeter of the triangle?

### Minimizing and Maximizing Area

A wire length L cm, is cut into 2 parts. One piece forms a rectangle whose length is twice its width and the other piece forms an equilateral triangle. How should the wire be cut so that the total area is a A) maximum B) minimum

### Oblique Triangles and Identities

A) Verify the following Identities : i) [(Sin 2theta)/ (sin theta )- ( cos 2theta/ cos theta )] = sec theta ii) cos2x = (cot^2 x-1 )/ (cot^2 x-1 ) And, Ã¬Ã¬Ã¬) Use logarithms and the law of tangents to solve the triangle ABC, given that a= 21.46 ft, b= 46.28 ft, and C = 32Â° 28' 30

### Area of Oblique Triangles

A) Find the area of the isosceles triangle in which each of the equal sides is 14.72 in and the vertex angle is 47Â° 28' . B) Find the radius of the inscribed circle and the radius of the circumscribed circle for the following obliqe triangle : a) = 12.7 , b = 21.5, and c = 28.6

### Oblique Triangles

Using LOGARITHMS, find the area of the following triangles : a) a = 12.7, b = 21.5, and c = 28.6 b) c = 426, A = 45Â° 48' 36 " , and B = 61Â° 2' 13 ".

### Explain how to compute the volume of a regular tetrahedron of edge length 1.

Euclidean Geometry (II) Computing the Volume of a regular tetrahedron of edge length 1 Explain how to compute the volume of a regular tetrahedron of edge length 1.

### The Volume of a Tetrahedron

Computing the Volume of a regular tetrahedron of edge length 2(alpha). Explain how to compute the volume of a regular tetrahedron of edge length 2(alpha).

### Cutting a Circle into Triangles

If there are n points on the circumference of a "cake" and each pair of these points is joined by a line or "cut" Let Wn be the number of regions. In the attached picture W4 = 8 (points ABCD). If we add point E and join it to every other point. Consider how many regions the segment AED is split into and then triangles ABC and AB

### Find the volume of a tetrahedron and an octahedron.

I need help writing a proof of the formulas of the volumes of two regular polyhedra (Platonic solids): (1) a tetrahedron and (2) an octahedron. I then have to use those formulas to find the volumes given a side length of 1.

### Lengths and Angles of a Triangle

Solve the triangle, round lengths to the nearest tenth and angle measures to the nearest degree. Please show work and see attachment.

### Solve the triangle, round lengths to the nearest tenth and angle measures to the nearest degree.

Please see attachment and show work.

### Sin Rule for Triangles and Solving Trignometric Functions

See the attached file. Solve the triangle. Round lengths to the nearest tenth and degrees. 1. B = 43, C = 107, B = 14 2. C = 110, a = 5, b = 11 3. B = 54, C = 112, b = 35 Find the solution 2 cos(theta) + 1 = 0.

### Determine graphically the vertices of the triangle.

Determine graphically the vertices of the triangle , the equations of whose sides are y=x; y=0; 2x+3y=10

### Perimeter of a Triangle With Square Roots

One is the square root of 5-3, One is the square root of 5+3, One is 4

### Isosceles Triangle

Please see the attached file for full question.

### Geometry Questions

See attached file for full problem description.

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

### Circles and Inscribed Right Triangles

Please see the attached file for the fully formatted problems.

### Finding the Sides of a Triangle

The hypotenuse of a right triangle is 12 and the area is 16&#8730;5. Find the length of the legs of the triangle.

### Similar Triangles Measured

Surveying: Surveyors sometimes use similar triangles to measure inaccessible distances. A surveyor could find distance AB by setting up similar triangles ABC and EDC. Assuming all lengths may be directly measured to set up a proportion and solve for AB. 17. How does the surveyor make ABC similar to EDC? 18. Set up a prop

### Calculating Volume

6. What is the volume of a regular square pyramid which has a total area of 360 if the square base is 10 on a side. 9. How long is the edge of a cube whose total area is numerically equal to it's volume? 15. A cube has a cylinder inscribed inside of it. That cylinder has a sphere inscribed inside of it. What is the rati

### 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

### Finding the length of the side of a triangle.

Given ABC with a=38 degrees, b=25, and c=32, find the length of side a. Given ABC with a=4, b=5 and c=7, find the approximate size of the angle y