Chapter 8: Q.18 (page 553)

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” $a = 3, A = 10, b = 4$

Short Answer

Expert verified

The remaining sides and angles are $B = 13.3 C = 156.6 c = 6.86$

Step by step solution

Step 1. Given information

The given data is $a = 3, A = 10, b = 4$

Step 2. Find the angle B

Use the Law of sines, $\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c}$

Here, $a = 3, A = 10, b = 4$

$\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin 10}{3} = \frac{S i n B}{4} S i n B = \frac{4 * \sin 10}{3} S i n B = 0.23 B = 13.3$

Step 3. Find the angle C

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

$A + B + C = 180 10 + 13.3 + C = 180 C = 156.6$

Step 4. Find the length of side C

Use the Law of sines, $\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c}$

Here, $a = 3, A = 10, C = 156.6$

$\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin 10}{3} = \frac{S i n 156.6}{c} c = \frac{3 S i n 156.6}{\sin 10} c = 6.8$

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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.” $a = 3, A = 10, b = 4$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the angle B

Step 3. Find the angle C

Step 4. Find the length of side 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,A=10,b=4

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the angle B

Step 3. Find the angle C

Step 4. Find the length of side C

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Discrete Mathematics

Probability and Statistics

Mechanics Maths

Theoretical and Mathematical Physics

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.” $a = 3, A = 10, b = 4$