Chapter 8: Q. 34 (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 $b = 4, c = 5, B = 95 °$ .

Short Answer

Expert verified

No triangle is possible from the given measurements.

Step by step solution

Step 1. Given information

$b = 4, c = 5, B = 95 °$

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

$B y L a w o f S i n e s, F o r C, \frac{\Rightarrow \sin (B)}{b} = \frac{\sin (C)}{c} \Rightarrow \sin (C) = \frac{\sin (B) \times c}{b} = \sin (95 °) \times \frac{5}{4} = 0.9961 \times 1.25 = 1.245 S i n c e t h e r e i s n o a n g l e C f o r w h i c h \sin (C) > 1, t h e r e c a n b e n o t r i a n g l e w i t h t h e g i v e n m e a s u r e m e n t s .$

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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 $b = 4, c = 5, B = 95 °$ .

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 resultsb=4,c=5,B=95°.

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

Applied Mathematics

Probability and Statistics

Calculus

Geometry

Statistics

Logic and Functions

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 $b = 4, c = 5, B = 95 °$ .