Chapter 8: Q. 41 (page 535)

In the given problem solve the triangle using either the law of sines or law of cosines-
$b = 5, c = 12, A = 60 °$

Short Answer

Expert verified

Required values of the triangle are

$a = 10.44, B = 13.8 °, C = 34.75 °$

Step by step solution

Step 1. Given information

In the given triangle,

$b = 5, c = 12, A = 60 °$

We know Law of cosines,

$a^{2} = b^{2} + c^{2} - 2 b c \cos A$ ------- $(1)$

Also, Law of sines,

$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$ ------- $(2)$

Step 2. Calculation

For a, using equation $(1)$

$a^{2} = b^{2} + c^{2} - 2 b c \cos A \Rightarrow a^{2} = 5^{2} + 12^{2} - 2 \times 5 \times 12 . \cos 60 ° \Rightarrow a^{2} = 25 + 144 - 120 \times 0.5 \Rightarrow a^{2} = 109 \Rightarrow a = 10.44$

For B, using equation $(2)$

$\frac{\sin A}{a} = \frac{\sin B}{b} \Rightarrow \frac{\sin 60 °}{10.44} = \frac{\sin B}{5} \Rightarrow \frac{0.5}{10.44} = \frac{\sin B}{5} \Rightarrow \sin B = 0.239 \Rightarrow B = \sin^{- 1} (0.239) \Rightarrow B = 13.8 °$

For C, using equation $(2)$

$\frac{\sin A}{a} = \frac{\sin C}{c} \Rightarrow \frac{\sin 60 °}{10.44} = \frac{\sin C}{12} \Rightarrow \sin C = \frac{0.5 \times 12}{10.44} \Rightarrow \sin C = 0.57 \Rightarrow C = \sin^{- 1} (0.57) \Rightarrow C = 34.75 °$

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In the given problem solve the triangle using either the law of sines or law of cosines-
$b = 5, c = 12, A = 60 °$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

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In the given problem solve the triangle using either the law of sines or law of cosines-b=5,c=12,A=60°

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

Discrete Mathematics

Pure Maths

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

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-
$b = 5, c = 12, A = 60 °$