Chapter 8: Q.12 (page 553)

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” $a = 3, b = 5, B = 80$

Short Answer

Expert verified

The values are $a = 3 b = 5 c = 4.55 A = 36.2 B = 80 C = 63.8$

Step by step solution

Step 1. Given information

The given data is $a = 3, b = 5, B = 80$

Step 2. Find the angle A

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

Here, $a = 3, b = 5, B = 80$

$\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin A}{3} = \frac{S i n 80}{5} \sin A = \frac{3 * S i n 80}{5} \sin A = 0.59 A = 36.2$

Step 3. Find the angle C

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

$A + B + C = 180 36.2 + 80 + C = 180 C = 63.8$

.Find the side c

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

Here,role="math" localid="1647084215797" $a = 3, b = 5, A = 36.2, C = 63.8 \frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin 36.2}{3} = \frac{S i n 63.8}{c} c = 4.55$

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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.” $a = 3, b = 5, B = 80$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the angle A

Step 3. Find the angle C

.Find the 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,b=5,B=80

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the angle A

Step 3. Find the angle C

.Find the side c

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Decision Maths

Discrete Mathematics

Geometry

Mechanics Maths

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.” $a = 3, b = 5, B = 80$