Chapter 8: Q. 26 (page 528)

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve each triangle that results
$b = 4, c = 3, B = 40 °$ .

Short Answer

Expert verified

Only one triangle is possible.

Required valued of the triangle are $C_{1} = 28.82 °, A = 111.18 °, a = 5.8$

Step by step solution

Step 1. Given information

$b = 4, c = 3, B = 40 °$

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

$B y L a w o f S i n e s, F o r C, \frac{\Rightarrow \sin (B)}{b} = \frac{\sin (C)}{c} \Rightarrow \sin (C) = \frac{\sin (B) \times c}{b} = \sin (40 °) \times \frac{3}{4} = 0.6427 \times 0.75 = 0.482025 C_{1} \approx 28.82 ° o r C_{2} \approx 180 ° - 28.82 ° = 151.18 ° S i n c e, C_{1} + B < 180 °, △ A_{} B C_{1} i s p o s s i b l e a n d C_{2} + B > 180 °, △ A B C_{2} i s n o t p o s s i b l e . I n △ A B C_{1} : F o r A_{}, \Rightarrow A = 180 ° - B - C_{1} = 180 ° - 40 ° - 28.82 ° = 180 ° - 68.82 ° = 111.18 ° F o r a, \frac{\Rightarrow \sin (B)}{b} = \frac{\sin (A)}{a} \Rightarrow a = \frac{\sin (A) \times b}{\sin (B)} = \frac{\sin (111.18 °) \times 4}{\sin (40 °)} = \frac{0.9324 \times 4}{0.6427} = \frac{3.7296}{0.6427} = 5.8$

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Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve each triangle that results
$b = 4, c = 3, B = 40 °$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve each triangle that results b=4,c=3,B=40°.

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

Logic and Functions

Calculus

Decision Maths

Discrete Mathematics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve each triangle that results
$b = 4, c = 3, B = 40 °$ .