You have given an equal sided triangle with side length a. A straight line connects the center of the bottom side to the border of the triangle with an angle of a. Derive an expression fo the enclosed area A(a) with respect to the angle (see drawing). A A

You have given an equal sided triangle with side length a. A straight line connects the center of the bottom side to the border of the triangle with an angle of a. Derive an expression fo the enclosed area A(a) with respect to the angle (see drawing). A A

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter6: Circles

Section6.4: Some Constructions And Inequalities For The Circle

Problem 34E: A tangent ET is constructed to circle Q from external point E. Which angle and which side of...

See similar textbooks

Related questions

Q: Geometry Question

A: Given, Radius of cylinder = r = diameter / 2 = 7/2 m length of cylinder = h = 15 m So, volume of cy...

Q: Given the diagram above, determine the measures of x and g and the correct reasoning for each .

A: we know that angle x and 56∘ are alternate interior angle so, x=56∘ now sum of angle in a triangle ...

Q: number 20

Q: Rhombus ABCD has vertices A(1,1), B(5,3), C(7,7), and D(3,5). After a translation, the image A^1 is ...

A: The translated coordinates of (x,y) is: x=X+h y=Y+k Substitute the A(1,1) and A1(-2,8) as (x,y) and ...

Q: Reduce each equation to a standard form and describe the curve completely by providing the important...

Q: Please help with question

Q: Warm-up 1. Find the value of x if those angles are supplementary? to 118° X = 2. Find the value of x...

Q: Compute the median of 14, 18, 60, 42, 55, 35 Round to 2 decimal places as needed

Q: What is the range of the following: 65, 12, 37, 45, 24, 47 Round to 2 decimal places as needed.

A: Given The data is 65, 12, 37, 45, 24, 47 Arranging the data in ascending order : 12 , 24 , 37 , 45 ...

Q: Need

A: Given, ∆SDC ≅ ∆ORK CD = KR <SDC = <ORK So, from the side angle side rule we can prove that the...

Q: Show that the conjecture is false by finding a counter example in the space provided

A: A mathematical statement is false only requires finding one example where the statement isn't true. ...

Q: Need answers and explanation to both

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new quest...

Q: Show work

Q: 7. What is the best description of AB? altitude © perpendicular bisector median O angle bisector B

A: Altitude is the perpendicular line drawn from an angle of triangle to opposite side. Perpendicular b...

Q: There might be more than one answer for each one of them please include all answers

A: b=69, a=73 and B=46° By using Sine rule, we have asinA=bsinB⇒73sinA=69sin46°⇒sinA=73×sin46°69⇒sinA=0...

Q: If line n bisects CE, find CD. x + 6 4x - 21

A: It is given that line n bisects CE.Therefore,l(CD)=l(DE)

Q: Show work

Q: Please tell me what you know, because I do not understand these questions

A: a) If two lines are intersected by a transversal , then the bisector of any...

Q: Show answer

A: Given

Q: Triangle XYZ is Isosceles. Angle z is the vertex angle, XY = 21n -11, YZ = 30 - 2n, and XZ = 7n +3. ...

Q: Find the measure of the marked angles

A: We know that vertical angles are congruent. So from given figure we observe that, given two angles (...

Q: A right triangle has a hypotenuse of 30 inches and one leg that measures 24 inches. What is the leng...

Q: Struggling on this homework question. Is it C?

A: In ∆AEC and ∆BED,E is the mid point of AB. (given)AE = EB∠C≅∠D (Angle opposite to equal sides are e...

Q: Three cubes whose edges measure 3 cm, 4 cm, 5 cm respectively to form a single cube. Find its edge a...

Q: below are squares formed by matchsticks.

Q: This is my second time asking. So i already wasted a question. see attached what is rs and rt ...

Q: I'm new to line segments. Can someone help me with these problems?

A: As per bartleby guidelines more than one question is asked only the first question is to be solved. ...

Q: Need

Q: The diameter of the earth is approximately 7,920 miles; the diameter of the planet Jupiter (the larg...

Q: A copper wire 4 mm in diameter is evenly wound about a cylinder whose length is 24 cm and diameter 2...

Q: A 450 300 В D ABC üçgen, m(BAD) = 45° , m(DAC) = 30° ve 3|BD| = 2|DC| %3D what is |AB|/|AC|

Q: Which similarity postulate can be used to prove the triangles are similar?? How long will Chris's sh...

A: Given: Height of the lighthouse, BC=30 ft. Shadow of the lighthouse, AB=14 ft. Height of Chris, DE=6...

Q: Draw a map that shows the following route leading to buried treasure: Starting at the old tree, walk...

Q: Help

Q: 5. Find the v alue of x. 5x – 4 x + 6

A: Given : To determine : The value of x.

Q: Hi, Kindly help me with this question.

Question

You have given an equal sided triangle with side length a. A straight line connects the center
of the bottom side to the border of the triangle with an angle of a. Derive an expression fo
the enclosed area A(a) with respect to the angle (see drawing).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Basics (types, similarity, etc)$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

The center of a circle of radius 3 inches is at a distance of 20 inches from the center of a circle of radius 9 inches. What is the exact length of common internal tangent AB? HINT: Use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
Draw an obtuse triangle and, by construction, find its orthocentre. HINT: You will have to extend the sides opposite the acute angles.
a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing. bUse the relationship from part a to find CM, the length of the median to the hypotenuse of right ABC, in which mC=90, AC = 6, and BC = 8.
Circles O, P, and Q are tangent as shown at points X, Y, and Z. Being as specific as possible, explain what type of triangle PQO is if: a OX=2,PY=3,QZ=1 b OX=2,PY=3,QZ=2
Is it possible to draw a triangle whose sides measure a. 8, 9, and 10? b. 8, 9, and 17? c. 8, 9, and 18?
In ABC, M is the midpoint of AB and N is the midpoint of AC. If MN= 3x-11 and BC= 4x24, find the value of x._
In sphere O, the length of radius OP- is 6 in. Find the length of the chord: a QR- if QOR=90 b QS- if SOP=60
A circle is inscribed in a triangle having sides of lengths 5 in., 12 in., and 13 in. If the length of the radius of inscribed circle is 2 in., find the area of the triangle.
If the distance between -2, 3 and -2,a is 5 units, find all possible values of a.
Use a two-column proof to prove the following theorem: The lengths of the corresponding altitudes of similar triangles have the same ratio as lengths of any pair of corresponding sides. Given: DEFMNP; DG and MQ are altitudes Prove: DGMQ=DEMN