contestada

4) Solve ∆ABC, a = 2.5 cm, c = 3.6 cm, and ∠A = 43°. Begin by sketching and labelling
a diagram. Account for all possible solutions. Express each angle to the nearest
degree and each length to the nearest tenth of a unit.

5) Simplify the rational expression. No need to state restrictions.
[TIP: expand and simplify the numerator, leave the denominator in factored form]
[tex]\frac{5m-n}{2m+n} -\frac{4m^2 - 4mn + n^2}{4m^2-n^2}[/tex] ÷ [tex]\frac{3n+15m}{6m^2-mn-n^2}[/tex]

4 Solve ABC a 25 cm c 36 cm and A 43 Begin by sketching and labelling a diagram Account for all possible solutions Express each angle to the nearest degree and class=

Respuesta :

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:

[tex]\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}[/tex]

Given;

  • a = 2. 5cm
  • c = 3. 6cm
  • ∠A = 43°

Let's find angle C

[tex]\frac{sin 43}{2. 5} = \frac{sin C}{3. 6}[/tex]

cross multiply

0. 682 × 3. 6 = sin C × 2. 5

sin C = 2. 4552/ 2. 5

C = [tex]sin^-^1(0. 982)[/tex]

C = 79°

To find length of b

[tex]b= \sqrt{c^2 - a^2}[/tex]

substitute the values

[tex]b = \sqrt{3.6^2 - 2. 5^2}[/tex]

[tex]b = \sqrt{6. 71}[/tex]

b = 2. 59 cm

b = 3cm

To find angle B, we have

[tex]\frac{sin 43}{2. 5} = \frac{sin B}{2. 59}[/tex]

cross multiply

0. 682 × 2. 59= sin B × 2. 5

sin B = 0. 7065

[tex]B = sin^-^1(0. 7065)[/tex]

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:

https://brainly.com/question/12827625

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