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# Triangles

### Right triangle

For the right triangle, find the side length x. Round answer to nearest tenth. Base=x Side=14 Side=8

### Side length for right triangle

For a right triangle, find the side length x round to the nearest tenth. Side: x Side: 6 Base: 9

### 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'.

### Construction and Geometry Proofs

1. I need to see a construction and proof. Given a quadrilateral EFGH so that all four sides are congruent to a circle. Prove that EF+GH=EH+FG 2. Prove that a perpendicular bisector of a chord in a circle is a diameter.

### 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

### Length of the hypotenuse of the right triangle ABC

What is the length of the hypotenuse of the right triangle ABC in examination figure,if AC=6 and AD=5 note : draw a triangle A B C and the height from point C to D,the point D is in between A and B,the distance between A and D is 5 and the distance between A and C is 6

### 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

### I am confused with understanding matrices in these problems: Explain matrices and triangles

1) A ranger in fire tower A spots a fire at a direction of 295 degrees. A ranger in fire tower B, located 45 miles at a direction of 45 degrees from tower A, spots the same fire at direction of 255 degrees. How far from tower A is the fire? From tower B? 2) In mountain communities, helicopters drop chemical retardants over a

### Word problem

(See attached file for full problem description) The area A of an equilateral triangle varies directly as the square of the length of a side. If the area of the equilateral triangle whose sides are of length 2 cm is (&#8730;3) cm2 , find the length s of an equilateral triangle whose area A is (&#8730;3)/4 cm2.

### Solving Radical Equations and Finding Side of a Cube Given Volume

1) Solve the following equations. a) Answer: Show work in this space. b) Answer: Show work in this space. c) Answer: Show work in this space. 2) Is an identity (true for all nonnegative values of x)? Answer: Explain your answer in this space. 3) For the equa

### Geometry

(See attached file for full problem description with proper symbols) The area A of an equilateral triangle varies directly as the square of the length of a side. If the area if the equilateral triangle whose sides are of length 1 cm is ( &#61654; 3 ) / 4 cm 2 , find the length s of an equilateral triangle whose area A is

### Slant height of sides of isosceles triangle

Question re slant height of ski lodge roof - isosceles triangle, base is 14 m. Vertical angle is 36 degrees. What would slant height of sides of roof (triangle) be, i.e., side AC or side BC?

### Finding the slant height of isosceles triangle

A ski chalet roof is isosceles triangle and has a vertical angle of 36 degrees. Width of base is 14 m. What is the slant height of roof? keywords: hypotenuse, pythagorean, pythagorus, theorem

### Conditional Inequality in a Triangle

In a triangle ABC, Angles are given in a particular order. Each angle is an acute angle. A number M is defined as Cos(A-B)/2SinA/2SinB/2. Find the minimum value of M.

### Finding an angle of a right-triangle.

The sides of a right triangle are 4 and 12. How do I get the angle?

### Distinct Points in a 9-Point Circle

How many distinct points does the 9-point circle have when the triangle is - isosceles - equlateral - right-angled isosceles.

### 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.

### Applications of Trigonometery Word Problems : Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point?

Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point?

### 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.

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

### Matrix & Vector Problem : Find the area of the triangle with vertices...; Compute the volume of the tetrahedron with vertices...

(a) (i) Find the area of the triangle with vertices (t, t-2), (t+2. t+2). (t-3, t) Does the area changes with t? (ii) In a theorem of solid geometry, the volume of the tetrhedron is 1/3 (base area )x( height). Compute the volume of the tetrahedron with vertices A( -1, 2, 0), B=(3, 5, 1), C(0, 0, 1) and D=(4.-1, 3). Hint

### 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.

### Proof : Incircle and Triangle - Menelaus Theorem

The incircle of triangle ABC touches the sides BC, CA, AB at the points x,y,z respectively. yz is produced to meet BC at k. Show that Bx/Cx = Bk/Ck.

### 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