Chapter 8: Q.11 (page 507)

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” $a = 3, c = 1, B = 100$

Short Answer

Expert verified

The value of $A = 62.8 b = 3.32 C = 17.2$

Step by step solution

Step 1. Given information

The given data is $a = 3, c = 1, B = 100$

Step 2. Find the side b

Use cosines rule $\cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c}$

Here, $a = 3, c = 1, B = 100$

$\cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c} \cos 100 = \frac{3^{2} + 1^{2} - b^{2}}{2 * 3 * 1} (- 0.17) * 6 = 10 - b^{2} b^{2} = 10 + 1.02 b^{2} = 11.02 b = 3.32$

Step 3. Find the angle A

Using The Law of Sines $\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c}$

$\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin A}{3} = \frac{S i n 100}{3.32} \sin A = 0.89 A = 62.8$

Step 4.Find the angle C

Since the angle A,B,and c are the angel of a triangle ,

$A + B + C = 180 62.8 + 100 + C = 180 C = 180 - 162.8 C = 17.2$

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Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” $a = 3, c = 1, B = 100$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the side b

Step 3. Find the angle A

Step 4.Find the angle C

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Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” a=3,c=1,B=100

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the side b

Step 3. Find the angle A

Step 4.Find the angle C

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Mechanics Maths

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” $a = 3, c = 1, B = 100$