Explanation:
sin18
∘
)
=
x
(sin35
∘
)
Explanation:
Incomplete question:
\angle CBD = 53^\circ∠CBD=53
∘
\angle CAB = 35^\circ∠CAB=35
∘
AB = 75AB=75
See attachment for complete question
Required
Determine the equation to find x
First, is to complete the angles of the triangle (ABC and ACB)
\angle ABC + \angle CBD = 180∠ABC+∠CBD=180 --- angle on a straight line
\angle ABC + 53= 180∠ABC+53=180
Collect like terms
\angle ABC =- 53+ 180∠ABC=−53+180
\angle ABC =127^\circ∠ABC=127
∘
\angle ABC + \angle ACB + \angle CAB = 180∠ABC+∠ACB+∠CAB=180 --- angles in a triangle
\angle ACB + 127 + 35 = 180∠ACB+127+35=180
Collect like terms
\angle ACB =- 127 - 35 + 180∠ACB=−127−35+180
\angle ACB =18∠ACB=18
Apply sine rule
\frac{\sin A}{a} = \frac{\sin B}{b}
a
sinA
=
b
sinB
In this case:
\frac{\sin ACB}{AB} = \frac{\sin CAB}{x}
AB
sinACB
=
x
sinCAB
This gives:
\frac{(\sin 18^\circ)}{75} = \frac{(\sin 35^\circ)}{x}
75
(sin18
∘
)
=
x
(sin35
∘
)