Chapter 8: Q.17 (page 553)

Find the remaining angle(s) and side(s) of each triangle, if it (they) exists. If no triangle exists, say “No triangle.” $a = 1, b = \frac{1}{2}, c = \frac{4}{3}$

Short Answer

Expert verified

The remaining sides and angles are $A = 64 B = 26.7 C = 89.3$

Step by step solution

Step 1. Given information

The given data is $a = 1, b = \frac{1}{2}, c = \frac{4}{3}$

Step 2. Find the angle A

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

Here, $a = 1, b = \frac{1}{2}, c = \frac{4}{3}$

$c o s A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} \cos A = \frac{{(\frac{1}{2})}^{2} + {(\frac{4}{3})}^{2} - 1^{2}}{2 * \frac{1}{2} * \frac{4}{3}} \cos A = \frac{\frac{1}{4} + \frac{16}{9} - 1}{\frac{4}{3}} \cos A = \frac{\frac{9 + 48 - 36}{36}}{\frac{4}{3}} \cos A = \frac{21}{36} \times \frac{3}{4} \cos A = 0.43 A = 64$

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, $\frac{\sin A}{a} = \frac{S i n B}{b} = \frac{S i n C}{c} \frac{\sin 64}{1} = \frac{S i n B}{0.5} S i n B = 0.5 * \sin 64 S i n B = 0.44 B = 26.7$ $A = 64, a = 1, b = 0.5$

Step 4. Find the angle C

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

$A + B + C = 180 64 + 26.7 + C = 180 C = 89.3$

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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.” $a = 1, b = \frac{1}{2}, c = \frac{4}{3}$

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=1,b=12,c=43

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

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Decision 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.” $a = 1, b = \frac{1}{2}, c = \frac{4}{3}$