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The following figure shows an equllateral triangle Inscribed in a circle of radius 10 cm. Use the method of Example 6 in Section 6.2 to compute the area of the triangle. Give two forms for your answer: one with a square root and the other a calculator approximation rounded to two decimal places. cm? cm2

The following figure shows an equllateral triangle Inscribed in a circle of radius 10 cm. Use the method of Example 6 in Section 6.2 to compute the area of the triangle. Give two forms for your answer: one with a square root and the other a calculator approximation rounded to two decimal places. cm? cm2

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 49E: A lawn roller in the shape of a right circular cylinder has a radius of length 18 in. and a length...
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The following figure shows an equilateral triangle inscribed in a circle of radius 10 cm. Give two forms for your answer: one with a square root and the other a calculator approximation rounded to two decimal places.

 

p.s Example 5 is included as a guide to solve the problem. thank you

The following figure shows an equilateral triangle inscribed in a circle of radius 10 cm. Use the method of Example 6 in Section 6.2 to compute the area of the triangle. Give two forms for your answer: one with a square root and the other a calculator approximation rounded to two decimal places. cm2 = cm2
Transcribed Image Text:The following figure shows an equilateral triangle inscribed in a circle of radius 10 cm. Use the method of Example 6 in Section 6.2 to compute the area of the triangle. Give two forms for your answer: one with a square root and the other a calculator approximation rounded to two decimal places. cm2 = cm2
Figure 5 2 in. 2 in. A Solution The idea here is first to find the area of triangle BOA by using the area formula from Example 4. Then, since the pentagon is composed of five such identical triangles, the area of the pentagon will be five times the area of triangle BOA. We will make use of the result from geometry that, in a regular n-sided polygon, the central angle is 360° /n. In our case we therefore have 360° ZBOA = 5 : 72° We can now find the area of triangle BOA: area = ab sin 0 = ;(2) (2) sin 72° = 2 sin 72° in.? The area of the pentagon is five times this, or 10 sin 72° in.?. (Using a calculator, this is about 9.51 in.?.)
Transcribed Image Text:Figure 5 2 in. 2 in. A Solution The idea here is first to find the area of triangle BOA by using the area formula from Example 4. Then, since the pentagon is composed of five such identical triangles, the area of the pentagon will be five times the area of triangle BOA. We will make use of the result from geometry that, in a regular n-sided polygon, the central angle is 360° /n. In our case we therefore have 360° ZBOA = 5 : 72° We can now find the area of triangle BOA: area = ab sin 0 = ;(2) (2) sin 72° = 2 sin 72° in.? The area of the pentagon is five times this, or 10 sin 72° in.?. (Using a calculator, this is about 9.51 in.?.)
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