Chapter 8: Q.19 (page 553)

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” $a = 4, A = 20, B = 100$

Short Answer

Expert verified

The remaining sides and angles are $C = 60 b = 11.5 c = 10.1$ $C = 60 b = 11.5 c = 10.1$

Step by step solution

Step 1, Given information

The given data is $a = 4, A = 20, B = 100$

Step 2. Find the angle C

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

$A + B + C = 180 20 + 100 + C = 180 C = 180 - 120 C = 60$

Step 3. Find the length of side b

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

Here, $a = 4, A = 20, B = 100, C = 60$

$\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin 20}{4} = \frac{S i n 100}{b} b = \frac{4 S i n 100}{\sin 20} b = 11.5$

Step 4. Find the length of sides c

Use the Law of Sines , $\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin 20}{4} = \frac{S i n 60}{c} c = \frac{4 * S i n 60}{\sin 20} c = 10.1$

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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.” $a = 4, A = 20, B = 100$

Short Answer

Step by step solution

Step 1, Given information

Step 2. Find the angle C

Step 3. Find the length of side b

Step 4. Find the length of sides 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=4,A=20,B=100

Short Answer

Step by step solution

Step 1, Given information

Step 2. Find the angle C

Step 3. Find the length of side b

Step 4. Find the length of sides c

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

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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.” $a = 4, A = 20, B = 100$