Chapter 8: Q.20 (page 553)

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” $c = 5, b = 4, A = 70$

Short Answer

Expert verified

The remaining sides and angles are $a = 5.22 B = 46 C = 64$

Step by step solution

Step 1. Given information

The given data is $c = 5, b = 4, A = 70$

Step 2. Find the length of side a

Use the cosines rule of Law, $\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}$

Here, $c = 5, b = 4, A = 70$

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} \cos 70 = \frac{4^{2} + 5^{2} - a^{2}}{2 * 4 * 5} 0.34 = \frac{16 + 25 - a^{2}}{40} 0.34 * 40 = 41 - a^{2} a^{2} = 41 - 13.68 a^{2} = 27.32 a = 5.22$

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, $A = 70, a = 5.22, b = 4, c = 5$

$\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin 70}{5.22} = \frac{S i n B}{4} S i n B = 4 \frac{\sin 70}{5.22} S i n B = 0.72 B = 46$

Step 4. Find the angle C

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

$A + B + C = 180 70 + 46 + C = 180 C = 180 - 116 C = 64$

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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.” $c = 5, b = 4, A = 70$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the length of side 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.”c=5,b=4,A=70

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the length of side 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

Calculus

Statistics

Decision Maths

Probability and Statistics

Mechanics Maths

Applied Mathematics

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.” $c = 5, b = 4, A = 70$