Chapter 8: Q. 18 (page 527)

In the given problem solve the triangle using the law of sines : $A = 50 °, C = 20 °, a = 3$ .

Short Answer

Expert verified

Required values of the triangle are $B = 110 °, c = 1.3, b = 3.7$ .

Step by step solution

Step 1. Given information

For a triangle with sides a, b, c and opposite angles A, B, C, respectively, Law of sines is given as:

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

Step 2. Calculation

$G i v e n, A = 50 °, C = 20 °, a = 3 F o r c, A c c o r d i n g t o L a w o f \sin e s \Rightarrow \frac{\sin (A)}{a} = \frac{\sin (C)}{c} \Rightarrow c = \frac{\sin (C) \times a}{\sin (A)} = \frac{\sin (20 °) \times 3}{\sin (50 °)} = \frac{0.342 \times 3}{0.766} = \frac{1.026}{0.766} = 1.339 \approx 1.3 F o r B, \Rightarrow B = 180 ° - A - C = 180 ° - 50 ° - 20 ° = 180 ° - 70 ° = 110 ° F o r b, A c c o r d i n g t o L a w o f \sin e s \Rightarrow \frac{\sin (A)}{a} = \frac{\sin (B)}{b} \Rightarrow b = \frac{\sin (B) \times a}{\sin (A)} = \frac{\sin (110 °) \times 3}{\sin (50 °)} = \frac{0.9396 \times 3}{0.766} = 3.679 \approx 3.7$

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In the given problem solve the triangle using the law of sines : $A = 50 °, C = 20 °, a = 3$ .

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 the law of sines :A=50°,C=20°,a=3.

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

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Pure Maths

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the given problem solve the triangle using the law of sines : $A = 50 °, C = 20 °, a = 3$ .