Question

4) Solve ∆ABC, a = 2.5 cm, c = 3.6 cm, and ∠A = 43°. Begin by sketching and labelling

Answer 1

The length of b and angle B and C are 2. 9cm, 44. 9  degrees and 79. 11 degrees respectively.

How to determine the parameters

To determine the angles and length of sides, we use the sine rule

The sine rule is thus:

$\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}$

Given;

• a = 2. 5cm
• c = 3. 6cm
• ∠A = 43°

Let's find angle C

$\frac{sin 43}{2. 5} = \frac{sinC}{3. 6}$

cross multiply

0. 682 × 3. 6 = sin C × 2. 5

sin C = 2. 4552/ 2. 5

C = $sin^-^1( 0. 98206)$

C = 79. 11°

To find length of b

b = $\sqrt{c^2 - a^2}$

substitute the values

b = $\sqrt{3. 6^2 - 2. 5^2}$

b = $\sqrt{12. 96 - 6. 25 }$

b = $\sqrt{6. 71}$

Take square root

b = 2. 59 cm

To find angle B, we have

$\frac{sin 43}{2. 5} = \frac{sin B}{2. 59}$

cross multiply

0. 682 × 2. 59= sin B × 2. 5

sin B = 0. 7066

B = $sin^-^1 ( 0. 7066)$

B = 44. 9 °

Thus , the length of b and angle B and C are 2. 9cm, 44. 9  degrees and 79. 11 degrees respectively.

Learn more about sine rule here:

brainly.com/question/12827625

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