Chapter 8: Q.16 (page 553)

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

Short Answer

Expert verified

The remaining sides and angles are $B = 36.2 C = 63.8 c = 4.55$

Step by step solution

Step 1. Given information

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

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, $a = 5, b = 3, A = 80$

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

Step 3. Find the angle C

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

Here, $A = 80, B = 36.2$

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

Step 4. find the side c

Use the Law of Sines $\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin 80}{5} = \frac{S i n 63.8}{c} c = 5 \frac{\sin 63.8}{\sin 80} c = 4.55$

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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.” $a = 5, b = 3, A = 80$

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 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=5,b=3,A=80

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 side c

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Pure Maths

Geometry

Decision Maths

Logic and Functions

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.” $a = 5, b = 3, A = 80$