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Vikentia [17]
2 years ago
15

Help me pleaseeeeeeeeeeeeeeeeeeeee

Mathematics
2 answers:
artcher [175]2 years ago
6 0

Answer:

a = 16.5 cm (nearest tenth)

b = 23.8 cm (nearest tenth)

Step-by-step explanation:

<u>Definition</u>

A, B and C are the angles and a, b and c are the sides opposite the angles.

From inspection of the triangle:

  • A = 42°
  • B = 75°
  • c = 22 cm

<u>Interior angles of a triangle sum to 180°</u>:

⇒ A + B + C = 180°

⇒ 42° + 75° + C = 180°

⇒ C = 180° -  117°

⇒ C = 63°

To find the missing <u>side lengths</u> a and b, use the Sine Rule:

\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}

<u>Substitute</u> the given values into the <u>Sine Rule formula</u>:

\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}

<u>Finding side a</u>:

\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{22}{\sin 63^{\circ}}

\implies \sf a=\dfrac{22\sin 42^{\circ}}{\sin 63^{\circ}}

\implies \sf a=16.52162239...

Therefore, side a is 16.5 cm (nearest tenth).

<u>Finding side b</u>:

\implies \sf \dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}

\implies \sf b=\dfrac{22\sin 75^{\circ}}{\sin 63^{\circ}}

\implies \sf b=23.84984577...

Therefore, side b is 23.8 cm (nearest tenth).

Learn more about the Sine Rule here:

brainly.com/question/28033514

brainly.com/question/27704834

vladimir1956 [14]2 years ago
5 0

Answer:

  • a = 16.52 cm
  • b = 23.85 cm

=========================

<h2>Given </h2>

  • AB = 22 cm
  • m∠A = 42°
  • m∠B = 75°

<h2>To find</h2>

  • Side length of a and b

<h2>Solution</h2>

The law of sines is:

  • a/sin A = b/sin B = c/sin C

<h3>Step 1</h3>

Find the value of ∠C using the angle sum theorem:

  • m∠A + m∠B + m∠C = 180°
  • 42° + 75° + C = 180°
  • 117° + C = 180°
  • C = 180° - 117°
  • C = 63°

<h3>Step 2</h3>

Find side a:

<u>Note</u>, the sides of a triangle are marked as:

  • a = BC, b = AC, c = AB (opposite to respective angle).

Use two pairs with one unknown:

  • a/sin A = c/sin C

Substitute values and solve for a:

  • a/ sin 42° = 22/sin 63°
  • a = 22*sin 42°/sin 63°
  • a = 16.52 cm (rounded)

<h3>Step 3</h3>

Find side b, similar to finding side a:

  • b/ sin 75° = 22/sin 63°
  • b = 22*sin 75°/sin 63°
  • b = 23.85 cm (rounded)
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