Elementary Geometry for College Students
6th Edition
ISBN: 9781285195698
Author: Daniel C. Alexander, Geralyn M. Koeberlein
Publisher: Cengage Learning
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Chapter 11.4, Problem 44E
To determine
To Prove:
The area of the equilateral
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Chapter 11 Solutions
Elementary Geometry for College Students
Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 7 to 14, use either Table 11.2 or a...Ch. 11.1 - In Exercises 7 to 14, use either Table 11.2 or a...Ch. 11.1 - Prob. 9ECh. 11.1 - Prob. 10E
Ch. 11.1 - In Exercises 7 to 14, use either Table 11.2 or a...Ch. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - In Exercises 15 to 20, find the lengths of the...Ch. 11.1 - In Exercises 15 to 20, find the lengths of the...Ch. 11.1 - Prob. 17ECh. 11.1 - In Exercises 15 to 20, find the lengths of the...Ch. 11.1 - In Exercises 15 to 20, find the lengths of the...Ch. 11.1 - Prob. 20ECh. 11.1 - In Exercises 21 to 26, find the measures of the...Ch. 11.1 - Prob. 22ECh. 11.1 - In Exercises 21 to 26, find the measures of the...Ch. 11.1 - Prob. 24ECh. 11.1 - In Exercises 21 to 26, find the measures of the...Ch. 11.1 - Prob. 26ECh. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - Prob. 33ECh. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - For Exercises 35 to 38, make drawings as needed....Ch. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.2 - In Exercises 1 to 6, find cos and cos.Ch. 11.2 - In Exercises 1 to 6, find cos and cos.Ch. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - In Exercises 1 to 6, find cos and cos.Ch. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - In Exercise 17 to 22, use either the sine ratio or...Ch. 11.2 - In Exercise 17 to 22, use either the sine ratio or...Ch. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - In Exercise 17 to 22, use either the sine ratio or...Ch. 11.2 - In Exercise 23 to 28, use either the sine ratio or...Ch. 11.2 - In Exercise 23 to 28, use either the sine ratio or...Ch. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - In Exercise 29 to 37, angle measures should be...Ch. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - In Exercise 29 to 37, angle measures should be...Ch. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - For Exercise 42 and 43, use the drawing and the...Ch. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.3 - In Exercises 1 to 4, find tan and tan for each...Ch. 11.3 - In Exercises 1 to 4, find tan and tan for each...Ch. 11.3 - In Exercises 1 to 4, find tan and tan for each...Ch. 11.3 - Prob. 4ECh. 11.3 - In Exercises 5 to 10, find the value or expression...Ch. 11.3 - In Exercises 5 to 10, find the value or expression...Ch. 11.3 - In Exercises 5 to 10, find the value or expression...Ch. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - In Exercises 15 to 20, use the sine, cosine, or...Ch. 11.3 - In Exercises 15 to 20, use the sine, cosine, or...Ch. 11.3 - Prob. 21ECh. 11.3 - In Exercises 21 to 26, use the sine, cosine, or...Ch. 11.3 - In Exercises 21 to 26, use the sine, cosine, or...Ch. 11.3 - Prob. 24ECh. 11.3 - In Exercises 21 to 26, use the sine, cosine, or...Ch. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - In Exercises 27 to 32, use a calculator and...Ch. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.3 - Prob. 40ECh. 11.3 - Prob. 41ECh. 11.3 - In Exercises 37 to 43, angle measures should be...Ch. 11.3 - In Exercises 37 to 43, angle measures should be...Ch. 11.3 - Prob. 44ECh. 11.3 - Prob. 45ECh. 11.3 - Prob. 46ECh. 11.3 - Prob. 47ECh. 11.4 - In Exercises 1 and 2, use the given information to...Ch. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - In Exercises 3 and 4, state the form of the Law of...Ch. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - In Exercises 15 and 16, find the area of the given...Ch. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - In Exercises 29 to 34, use the Law of Sines or the...Ch. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Prob. 36ECh. 11.4 - Prob. 37ECh. 11.4 - Show that the form of the Law of Cosines written...Ch. 11.4 - Explain why the area of the parallelogram shown is...Ch. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.CR - In Exercises 1 to 4, state the ratio needed, and...Ch. 11.CR - In Exercises 1 to 4, state the ratio needed, and...Ch. 11.CR - In Exercises 1 to 4, state the ratio needed, and...Ch. 11.CR - Prob. 4CRCh. 11.CR - In Exercises 5 to 8, state the ratio needed, and...Ch. 11.CR - In Exercises 5 to 8, state the ratio needed, and...Ch. 11.CR - In Exercises 5 to 8, state the ratio needed, and...Ch. 11.CR - In Exercises 5 to 8, state the ratio needed, and...Ch. 11.CR - In Exercises 9 to 12, use the Law of Sines or the...Ch. 11.CR - Prob. 10CRCh. 11.CR - In Exercises 9 to 12, use the Law of Sines or the...Ch. 11.CR - Prob. 12CRCh. 11.CR - Prob. 13CRCh. 11.CR - Prob. 14CRCh. 11.CR - Prob. 15CRCh. 11.CR - Prob. 16CRCh. 11.CR - Prob. 17CRCh. 11.CR - Prob. 18CRCh. 11.CR - Prob. 19CRCh. 11.CR - Prob. 20CRCh. 11.CR - In exercises 21 to 30. Use the drawings. Where...Ch. 11.CR - In exercises 21 to 30. Use the drawings. Where...Ch. 11.CR - In exercises 21 to 30. Use the drawings. Where...Ch. 11.CR - In Exercises 21 to 30, use the drawings, where...Ch. 11.CR - Prob. 25CRCh. 11.CR - Prob. 26CRCh. 11.CR - Prob. 27CRCh. 11.CR - Prob. 28CRCh. 11.CR - Prob. 29CRCh. 11.CR - In Exercises 21 to 30, use the drawings, where...Ch. 11.CR - Prob. 31CRCh. 11.CR - Prob. 32CRCh. 11.CR - Prob. 33CRCh. 11.CR - Prob. 34CRCh. 11.CT - Prob. 1CTCh. 11.CT - Prob. 2CTCh. 11.CT - Prob. 3CTCh. 11.CT - Prob. 4CTCh. 11.CT - Using your calculator, find to the nearest degree...Ch. 11.CT - Without the calculator, determine which number is...Ch. 11.CT - Prob. 7CTCh. 11.CT - Prob. 8CTCh. 11.CT - Prob. 9CTCh. 11.CT - Prob. 10CTCh. 11.CT - Prob. 11CTCh. 11.CT - Prob. 12CTCh. 11.CT - Prob. 13CTCh. 11.CT - Prob. 14CTCh. 11.CT - Prob. 15CTCh. 11.CT - Prob. 16CTCh. 11.CT - Prob. 17CTCh. 11.CT - Prob. 18CTCh. 11.CT - Prob. 19CTCh. 11.CT - Prob. 20CT
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- The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle of radius length 3 inches. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.arrow_forwardEach side of square RSTV has length 8. Point W lies on VR- and point Y lies on TS- in such a way to form parallelogram VWSY, which has an area of 16units2. Find the length of VW-.arrow_forwardFind the area of an equilateral triangle with apothem a = 3.2 cm and perimeter P=19.23 cm.arrow_forward
- A rectangular solid has length L=12.6 mm, width W=23.8 mm, and height H=32.5 mm. Find the length of a diagonal AB from the upper left rear vertex to the lower right front vertex. Round the answer to 1 decimal place.arrow_forwardProve that the altitude drawn to the hypotenuse of a right triangle separates the right triangle into two right triangles that are similar to each other and to the original right triangle.arrow_forwardThe larger circle is inscribed in a square with sides of length 4cm. The smaller circle is tangent to the larger circle and to two sides of the square, as shown. Find the length of the radius of the smaller circle.arrow_forward
- 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.arrow_forwardFind the area of an equilateral triangle with apothem a = 4.6 in. and perimeter P=27.63 in.arrow_forwardComplete an analytic proof of the following theorem: In a triangle that has sides of lengths a,b, and c, if c2=a2+b2, then the triangle is a right triangle.arrow_forward
- Which part hypothesis or conclusion of a theorem determines the a Drawing? b Given? c Prove?arrow_forwardThe center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of radius length 3 in. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.arrow_forwardMeasure the lengths of dimensions a-f in Figure 30-25 to the nearer whole millimeter.arrow_forward
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