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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.17 (page 553)

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say 鈥淣o triangle.鈥� $a = 1, b = \frac{1}{2}, c = \frac{4}{3}$

Short Answer

Expert verified

The remaining sides and angles are $A = 64 B = 26.7 C = 89.3$

Step by step solution

01

Step 1. Given information

The given data is $a = 1, b = \frac{1}{2}, c = \frac{4}{3}$

02

Step 2. Find the angle A

Use the Law of cosines, $\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}$

Here, $a = 1, b = \frac{1}{2}, c = \frac{4}{3}$

$c o s A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} \cos A = \frac{{(\frac{1}{2})}^{2} + {(\frac{4}{3})}^{2} - 1^{2}}{2 * \frac{1}{2} * \frac{4}{3}} \cos A = \frac{\frac{1}{4} + \frac{16}{9} - 1}{\frac{4}{3}} \cos A = \frac{\frac{9 + 48 - 36}{36}}{\frac{4}{3}} \cos A = \frac{21}{36} 脳 \frac{3}{4} \cos A = 0.43 A = 64$

03

Step 3. Find the angle B

Use the Law of Sines, $\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c}$

Here, $\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin 64}{1} = \frac{S i n B}{0.5} S i n B = 0.5 * \sin 64 S i n B = 0.44 B = 26.7$ $A = 64, a = 1, b = 0.5$

04

Step 4. Find the angle C

Since the angle A, B, and c are the angel of a triangle,

$A + B + C = 180 64 + 26.7 + C = 180 C = 89.3$

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Most popular questions from this chapter

Rework Problem 6 under the same conditions except that, at time t = 0, the object is at its resting position and moving down.

What do you do first if you are asked to solve a triangle and are given two sides and the angle opposite one of them?

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?

Find the real solutions, if any, of the equation $3 x^{2} + 1 = 4 x$ .

An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down a distance a (in centimeters) from its rest position and then released. Assume that the positive direction of the motion is up and the period is T (in seconds) under simple harmonic motion.

(a) Develop a model that relates the distance d of the object from its rest position after t seconds.

(b) Graph the equation found in part (a) for 5 oscillations using a graphing utility.

Given values: $m = 20, a = 15, b = 0.75, T = 6$

See all solutions

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