Chapter 8: Q. 39 (page 535)

In the given problem solve the triangle using either the law of sines or law of cosines-
$A = 10 °, a = 3, b = 10$

Short Answer

Expert verified

Required values of the triangle are $B = 35.35 °, C = 134.65 °, c = 12.29$

Step by step solution

Step 1. Given information

In the given triangle,

$A = 10 °, a = 3, b = 10$

We know, Law of sines

$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$ ------role="math" localid="1646587025370" $(1)$

Law of cosines,

$c^{2} = a^{2} + b^{2} - 2 a b \cos C$ ------ $(2)$

Step 2. Calculation

$F o r B, \frac{\sin A}{a} = \frac{\sin B}{b} \sin B = \frac{\sin A \times b}{a} = \sin (10 °) \times \frac{10}{3} = \frac{0.1736 \times 10}{3} = \frac{1.736}{3} = 0.5786 B = \sin^{- 1} (0.5786) = 35.35 ° F o r C, C = 180 ° - A - B = 180 ° - 10 ° - 35.35 ° = 134.65 ° F o r c, c^{2} = a^{2} + b^{2} - 2 a b \cos (C) = 3^{2} + 10^{2} - 2 \times 3 \times 10 \times \cos (134.65 °) = 9 + 100 - 60 \times (- 0.7027) = 151.162 c = \sqrt{151.162} = 12.29$

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In the given problem solve the triangle using either the law of sines or law of cosines-
$A = 10 °, a = 3, b = 10$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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In the given problem solve the triangle using either the law of sines or law of cosines-A=10°,a=3,b=10

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Discrete Mathematics

Statistics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the given problem solve the triangle using either the law of sines or law of cosines-
$A = 10 °, a = 3, b = 10$