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# Triangles

### Value of Theta: Maximum Area of Triangle

An isosceles triangle has two equal sides of length 10cm. Let theta be the angle between the two equal sides. The Area of the triangle can be expressed as: A(theta) = 50sin(theta) If theta is increasing at the rate of 10 degrees per minute (pie/18 radians per minute)and the derivative of the area is [50cos(theta)]at what valu

### Equilateral Triangle Problem

Let's say you hgave an area with 100 feet of fence. Two configurations were a circle and a rectangle. What other possibilities of utilizing other shapes for this fenced in area. Could you create a figure with a larger area than the circle? In particular an equilateral triangle: A=(1/4) (s 2nd power) (3 1/2 power)where S is th

### Centroid theorem proof and deriving the distance formula

Prove the CENTROID therorem using the VECTOR proof as well as the SYNTHETIC proof Explain how to derive the distance formula (assuming that the distance formula is not yet known), first in 2 dimentional and then in 3 dimentional

### Geometry problems

What is a polygon? What is the difference between an equiangular polygon, an equilateral polygon, and a regular polygon? Provide an example of each. 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 th

### Geometry Problems

Please correct and explain. 1. Are the angles of a triangle considered to be supplementary? _Yes Explain your answer. Any two angles that add up to 180 degrees are known as supplementary angles. Three angles inside any triangle always add up to 180 degrees. Classify the following as true or false. If false, tell why

### Geometry in Real-Life

For geometry I am having trouble to come up with an example for the question below that illustrate numbers. I need an example with numbers and some geometry calculations so that we can clearly see how geometry is used in our everyday life?

### Strategies for Teaching the Solving of Math Problems

Describe a general process that students in grades 5-8 or 9-12 can use to solve problems. B. Describe at least five specific problem-solving strategies that these students can use to solve mathematics problems. For each strategy, give an example. C. Discuss how these strategies and processes encourage students to persist

### Metric Space Proofs

Problem 1: Given the metric space (X, p), prove that a) |p(x, z) - p(y, u)| < p(x, y) + p(z, u) (x, y, z, u is an element of X); b) |p(x, y) - p(y, z)| < p(x, y) (x, y, z is an element of X). These problems are from Metric Space. Please give formal proofs for both (a) and (b) based on the reference provided. Thank y

### Word Problem Involving Tangent Function

A patient is being treated with laser therapy to remove a tumour that is located behind a vital organ. The tumor is 5.7 cm below the skin. To avoid the organ, the entry point of the laser must be 12.4 cm above the tumour along the skin. What is the angle the doctor must use to hit the tumor directly? Round your anwer to the near

### Mathematics - Geometry - Pythogorean Theorem

1) A right triangle is a triangle with one angle measuring 90^o. In a right triangle, the sides are related by Pythagorean Theorem, , where c is the hypotenuse (the side opposite the 90^o angle). Find the hypotenuse when the other 2 sides' measurements are 6 feet and 8 feet. 2)Suppose you travel north for 65 kilometers then t

### Geometry : Polygons and Geoboards

26. On a sheet of dot paper or on a geoboard like the one shown, create the following: a. Right angle b. Acute angle c. Obtuse angle 1. Adjacent angles e. Parallel segments 1. lntersecting segments Draw three different nonconvex polygons. When you walk around a polygon, at each vertex you need to turn either right (cloc

### Congruent and similar triangles

See attachment A. Find at least three examples of congruent objects in a typical classroom. (don't need pictures). What out of class activities could you employ to make students aware of congruent objects? Stan is standing on the bank of a river wearing a baseball cap. Standing erect and looking directly at th

### Real life examples of various types of triangles and graph

See attachment. Below is a list of various types of triangles: 1) Right triangle 2) Acute triangle 3) Obtuse triangle 4) Scalene triangle 5) Isosceles triangle 6) Equilateral triangle find an example of each of these triangles in your daily life. For example, Yield signs are a good example of acute

### Similar triangles geometry

Computing sides of similar triangles, locate a point when 2 angles are given.

### Find the height and base

The base of a triangle is 4 cm greater than the height. The area is 48 cm^2. Find the height and base of the triangle. The height of the triangle is ___ cm. The base of the triangle is ___ cm.

### Circle and Segment Proof

The lines AB, BC are tangent to the circle centered at O. The segment CE is perpendicular to the diameter BD. Show that |BE||BO|=|AB||CE| See attached for diagram.

### central angle of a circle of radius

1. a central angle of a circle of radius 30cm intercepts an arc of 6cm the central angle in terms of degrees is? 2. The reference angle of 3.22 rev? 3. When sin A and sec A are both negative, in what quadrant will you find its terminal side? 4. In a right triangle abc. sin 2 = 5 / 13. find side b 5. if 0 is 3 / 4 o

### Using cross products to find orthogonal vectors and areas

Find a vector orthogonal to the plane through the points P, Q, and R and find the area of the triangle PQR. P(1,0,0) Q(0,2,0) R(0,0,3)

### Find the lengths of the sides of the triangle ABC

Find the lengths of the sides of the triangle ABC and determine whether the triangle is isosceles, a right triangle, both, or neither A(3,-4,1) B(5,-3,0) C(6,-7,4)

### Finding missing angle in a triangle

Solve for x where x is the measure of an angle in the following figure: I can't draw the triangle so I drew it on microsoft and attached the file. the measurements are degrees

### Trigonometry - Bearings/Courses

Two ships leave port at 7:00am. ship A sails on a 54° course at a rate of 36 mph. ship B sails on a 114° course at a rate of 42 mph. find the distance between the two ships at 11:00am and the bearing of ship B from ship A.

### Right triangle applications

1. a wall 9 feet cast a shadow of 15 feet. Find the angle of the sun's rays with the ground. 2. a point on the bank directly across the river is sighted from another point 200 feet downstream at an angle of 67° 13' . Find the width of the river.

### Distances and Angles - Find lengths of: Legs of triangle DEF

Find lengths of: Legs of triangle DEF perpendicular distance between F & D perpendicular distance between F & G perpendicular distance between E & G perpendicular distance between E & D And angles alpha, beta and/or pie.

### Find the symmetries of the regular tessellations in a plane

Square- we are to explain reflection: how many lines( 2 edges, 2 bisectors, vertex arrangement is order is 4 90degrees, rotation :center of shape is order 4, midpoint is order 2 180. triangle- reflection 6lines(3edges and 3 bisectors), vertex arrangement is very similar to hexagon but(please explain) order 6 (60 degrees)

### Vertex Figures and Arrangements

Find (and describe) all the regular tessellations of the plane. Note that septagons, nonagons, and 11-gons are not provided. How do you know each one you find really fills in all the gaps around a vertex point? How do you know when you're done? (2) Find (and describe) all the semiregular tessellations of the plane ( you will

### Geometry - Practice Problem

The Triangle is 30 degrees , -60 degrees, -90 degrees. Triangle ABC .A is at the top measuring 60 degrees, B is measuring 30 degrees and C is at the right angle. If b = 7cm , find a.

Please help write a formula, explained mathematically and show work. Show a drawing showing they repeat. Show examples of all 8 and go into detail please. Find (and describe) all the regular tessellations of the plane. Note that septagons, nonagons, and 11-gons are not provided. How do you know each one you find really fills

### relationship among three sides of a triangle

Please give a thorough explanation. Thanks. 1.Is it possible to have a triangle with sides measuring 10ft, 12 ft, and 23 ft.? 2.A mountain road is inclined 30 degrees with the horizontal, if a pick-up truck drives 2 mi. on this road , what change in altitude has been achieved?

### Explanation of how two isosceles triangles are similar.

Please give a through explanation to the following. thank you Answer true or false. a. If each of two isosceles triangles has an angle that measures 120 degrees, then the two isosceles triangles must be similiar. b. If each of two isosceles triangles has an angle that measures 40 degrees, then the two isosceles triangles m

### Circle Construction and Congruency- I am to draw any thee non collinear points. I am to construct a circle containing them on its circumference. I have drawn all of this. I have given each point a name A,B, C,D,E,F,G I am writing a paper and need to give an explanation as to why this is true or i need Proof that AD is congruent with DB and DB is congruent with DC. I am to use the triangle congruent of sss, sas, aas, asa, hl. I am to use the perpenicular bisector by defenitions, and reflexsive property and th CPCTC and double substitution and transit propeties.AGD IS CONGRUENT TO CGD and AD IS CONGRUENT TO CD AND CD IS CONGRUENT TO DB AND AD IS CONGRUENT TO DB. I AM TO EXPLAIN ALL OF THIS ON PAPER.

Circle constuction and Congruency I am to draw any thee non collinear points. I am to construct a circle containing them on its circumference. I have drawn all of this. I have given each point a name A,B, C,D,E,F,G I am writing a paper and need to give an explanation as to why this is true or i need Proof that AD is congruent