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 3cm, 45  degrees and 79 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

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

cross multiply

0. 682 × 3. 6 = sin C × 2. 5

sin C = 2. 4552/ 2. 5

C = $sin^-^1(0. 982)$

C = 79°

To find length of b

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

substitute the values

$b = \sqrt{3.6^2 - 2. 5^2}$

$b = \sqrt{6. 71}$

b = 2. 59 cm

b = 3cm

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. 7065

$B = sin^-^1(0. 7065)$

B = 45°

Hence, the length of b and angle B and C are 3cm, 45  degrees and 79 degrees respectively.

Learn more about sine rule here:

brainly.com/question/12827625

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