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Oxana [17]
2 years ago
15

Please help i will give you 100 points

Mathematics
2 answers:
Cerrena [4.2K]2 years ago
8 0

Answer:

x = 50.5° (3 sf)

Step-by-step explanation:

<u>Sine Rule for side lengths</u>

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

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Find BD:

\implies \sf \dfrac{BD}{\sin BAD}=\dfrac{AB}{\sin BDA}

\implies \sf \dfrac{BD}{\sin 50^{\circ}}=\dfrac{5.6}{\sin 78^{\circ}}

\implies \sf BD=\dfrac{5.6\:sin 50^{\circ}}{\sin 78^{\circ}}

\implies \sf BD=4.385686657...cm

Angles on a straight line sum to 180°

⇒ ∠ADB + ∠BDC = 180°

⇒ 78° + ∠BDC = 180°

⇒ ∠BDC = 102°

<u>Sine Rule for angles</u>

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

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Find ∠BCD:

\implies \sf \dfrac{\sin BCD}{BD}=\dfrac{\sin BDC}{BC}

\implies \sf \dfrac{\sin BCD}{4.385...}=\dfrac{\sin 102^{\circ}}{9.3}

\implies \sf BCD=\sin^{-1}\left(\dfrac{4.385...\sin 102^{\circ}}{9.3}\right)

\implies \sf BCD=27.46935172...^{\circ}

The interior angles of a triangle sum to 180°

⇒ ∠CBD + ∠BDC + ∠BCD = 180°

⇒ x + 102° + 27.469...° = 180°

⇒ x = 50.53064828...°

⇒ x = 50.5° (3 sf)

svet-max [94.6K]2 years ago
5 0
<h3><u>Answer</u>:</h3>

x = 50.5°

<h3><u>Explanation</u>:</h3>

In order to solve, get to know about the sine rule:

\bf Sine \ Rule =  \dfrac{A}{sinA}  = \dfrac{B}{sinB}= \dfrac{C}{sinC}

<h3><u>Solve for BD</u>:</h3>

\sf \dfrac{BD}{sin(50)}  = \dfrac{5.6}{sin(78)}

\sf BD = \dfrac{5.6(sin(50))}{sin(78)}

\sf BD = 4.385686657 \ cm

Then find angle D = 180° - 78° = 102°

<h3><u>Solve for angle C</u></h3>

\sf \dfrac{4.385686657}{sinC}   = \dfrac{9.3}{sin(102)}

\sf C = sin^{-1}(\dfrac{4.385686657sin(102)}{9.3}  )

\sf C = 27.37 ^{\circ \:}

<h3><u>Total Sum of interior angles of a triangle is 180</u>°</h3>

\sf B + C + D = 180^\circ

\sf x + 27.37^\circ + 102^\circ = 180^\circ

\sf x = 180^\circ - 102^\circ - 27.37^\circ

\sf x = 50.53^\circ

\sf x = 50.5^\circ \ \ \  (rounded \ to \ nearest \ 3 \ significant \ figure)

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