Q. 77 Geometry Find the value of the a... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 8: Q. 77 (page 519)

Geometry Find the value of the angle $胃$ in degrees rounded to the nearest tenth of a degree.

Short Answer

Expert verified

The answer is $胃 = 38.9 掳 .$

Step by step solution

Step 1. Given information

We have two circles small circle have radius r1 = 2 and bigger circle have radius r2 = 4.

These two circle has two common tangents meeting at some point at an angle $胃$ .

Given:

$P S = 2 Q C = 4 鈭� P O S = 鈭� Q O C = \frac{胃}{2} . (S i n c e i t s y m m e t r i c a b o u t t h e l i n e d r a w n f r o m O) . S C = 2 + 4 = 6, A n d 鈭� O P S = 鈭� O Q C = 90 掳 . (S i n c e t h e \tan g e n t i s p e r p e n d i c u l a r t o t h e c i r c l e .)$

Step 2. Triangles and its properties

$I n 鈭� P O S, \sin (\frac{胃}{2}) = \frac{P S}{O S} . I n 鈭� Q O C, \sin (\frac{胃}{2}) = \frac{Q C}{O C} = \frac{Q C}{O S + S C} .$

Step 3. Solving the equations from step 2

$\sin (\frac{胃}{2}) = \frac{P S}{O S} = \frac{2}{O S}, N o w, \sin (\frac{胃}{2}) = \frac{Q C}{O S + S C}, \frac{2}{O S} = \frac{4}{O S + 6}, S o l v i n g f o r O S w e g e t, 2 O S + 12 = 4 O S, 2 O S = 12, O S = 6, N o w f r o m a b o v e e q u a t i o n, \sin (\frac{胃}{2}) = \frac{2}{O S} = \frac{2}{6} = \frac{1}{3}, \frac{胃}{2} = \sin^{- 1} (\frac{1}{3}), 胃 = 2 \sin^{- 1} (\frac{1}{3}), 胃 = 38.9424 . . . . 掳胃鈮� 38.9 掳 .$

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91影视

Geometry Find the value of the angle $胃$ in degrees rounded to the nearest tenth of a degree.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Triangles and its properties

Step 3. Solving the equations from step 2

One App. One Place for Learning.

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91影视

Geometry Find the value of the angle 胃in degrees rounded to the nearest tenth of a degree.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Triangles and its properties

Step 3. Solving the equations from step 2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Logic and Functions

Calculus

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Geometry Find the value of the angle $胃$ in degrees rounded to the nearest tenth of a degree.