Answered: 35° 15° A b 8 a = 13 В

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter8: Complex Numbers And Polarcoordinates

Section8.1: Complex Numbers

Problem 99PS

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Question

Solve the triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.

Expert Solution

Step 1

Given figure is,

Step 2

To solve the triangle.

That means to find side c, angle A, angle B, angle C.

Now first we find the angle C,

Now the sum of all angles on straight lines are $180^{\circ}$ .

$\Rightarrow 15^{\circ} + 35^{\circ} + a n g l e C = 180^{\circ} \Rightarrow 50^{\circ} + a n g l e C = 180^{\circ} \Rightarrow a n g l e C = 130^{\circ} .$

Now to find c by using cosine rule for c.

The cosine rule is, $c^{2} = a^{2} + b^{2} - 2 a b C o s C$ .

Substitute all values in $c^{2} = a^{2} + b^{2} - 2 a b C o s C$ ,

$c^{2} = 13^{2} + 8^{2} - 2 (13) (8) \cos (130^{\circ}) c^{2} = 233 - 208 (- 0.6427) c^{2} = 233 + 133.6816 c^{2} = 366.6816 \Rightarrow c = 19.1489 \Rightarrow c = 19$

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