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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 8: Q. 16 (page 535)

Solve the triangle

Short Answer

Expert verified

The solution is $A = 67.98 掳, B = 44.04 掳, C = 67.98 掳$

Step by step solution

01

Step2. Given information

$H e r e, a = 4, b = 3, c = 4$

02

Step2. Formula used

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}, \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c}$

03

Step3. Calculation

We know

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{3^{2} + 4^{2} - 4^{2}}{2.3.4} = \frac{9 + 16 - 16}{24} = \frac{9}{24} = . 375 A = \cos^{- 1} (. 375) = 67.98 掳 A g a i n, \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{4^{2} + 4^{2} - 3^{2}}{2.4.4} = \frac{16 + 16 - 9}{32} = \frac{23}{32} = . 71875 B = \cos^{- 1} (. 71875) = 44.04 掳 W e k n o w, A + B + C = 180 掳 67.98 掳 + 44.04 掳 + C = 180 掳 C = 180 掳 - 112.02 = 67.98 掳$

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Most popular questions from this chapter

Law of Tangents For any triangle, derive the Law of Tangents.

$\frac{a - b}{a + b} = \frac{\tan [\frac{1}{2} (A - B)]}{\tan [\frac{1}{2} (A + B)]}$

The displacement d (in meters) of an object at time t (in seconds) is given as $d = 5 \sin (3 t)$

(a) Describe the motion of the object.

(b) What is the maximum displacement from its resting position?

(c) What is the time required for one oscillation?

(d) What is the frequency?

The displacement d (in meters) of an object at time t (in seconds) is given $d = 6 \cos (蟺 t)$

(a) Describe the motion of the object.

(b) What is the maximum displacement from its resting position?

(c) What is the time required for one oscillation?

(d) What is the frequency?

The displacement d (in meters) of an object at time t (in seconds) is given $d = 4 \sin (2 t)$

(a) Describe the motion of the object.

(b) What is the maximum displacement from its resting position?

(c) What is the time required for one oscillation?

(d) What is the frequency?

Solve each triangle.

$a = 2, b = 2, c = 2$

See all solutions

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