Chapter 8: Q.14 (page 553)

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” $a = 10, b = 7, c = 8$

Short Answer

Expert verified

The value of the remaining angles are $A = 83.3 B = 44 C = 52.7$

Step by step solution

Step 1. Given information

The given data is $a = 10, b = 7, c = 8$

Step 2. Find the angle A

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

Here, $a = 10, b = 7, c = 8$

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} \cos A = \frac{7^{2} + 8^{2} - 10^{2}}{2 * 7 * 8} \cos A = \frac{49 + 64 - 100}{112} \cos A = \frac{13}{112} A = 83.3$

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, $A = 83.3, a = 10, b = 7$

$\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin 83.3}{10} = \frac{S i n B}{7} S i n B = \frac{7 \sin 83.3}{10} S i n B = 0.69 B = 44$

Step 4. Find the angle C

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

$A + B + C = 180 83.3 + 44 + C = 180 C = 180 - 127.3 C = 52.7$

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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.” $a = 10, b = 7, c = 8$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the angle A

Step 3. Find the angle B

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=10,b=7,c=8

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the angle A

Step 3. Find the angle B

Step 4. Find the angle C

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Applied Mathematics

Statistics

Calculus

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.” $a = 10, b = 7, c = 8$