Chapter 8: Q.15 (page 553)

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” $a = 1, b = 3, C = 40$

Short Answer

Expert verified

The remaining angles and sides of a triangle is $c = 2.32 A = 16 B = 124$

Step by step solution

Step 1. Given information

The given data is $a = 1, b = 3, C = 40$

Step 2. find the side c

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

Here. $a = 1, b = 3, C = 40$

$\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} \cos 40 = \frac{1^{2} + 3^{2} - c^{2}}{2 * 1 * 3} \cos 40 = \frac{10 - c^{2}}{6} 10 - c^{2} = 4.6 c^{2} = 5.4 c = 2.32$

Step 3. 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, $a = 1, b = 3, c = 2.32, C = 40$

$\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} . \frac{\sin A}{1} = \frac{S i n 40}{2.32} \sin A = 0.27 A = 16$

Step 4. Find the angle B

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

$A + B + C = 180 16 + B + 40 = 180 B = 180 - 56 B = 124$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” $a = 1, b = 3, C = 40$

Short Answer

Step by step solution

Step 1. Given information

Step 2. find the side c

Step 3. Find the angle B

Step 4. Find the angle B

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Decision 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=1,b=3,C=40

Short Answer

Step by step solution

Step 1. Given information

Step 2. find the side c

Step 3. Find the angle B

Step 4. Find the angle B

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Decision 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.” $a = 1, b = 3, C = 40$