Question

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Answer 1

1)

In ∆ABC,

Using the law of sines,

`\rightarrow (a)/( \sin(A) ) = (b)/( \sin(B) )`

where,

• a = 8cm
• b = ?
• Sin A = Sin 35
• Sin B = Sin 80

`\rightarrow (8cm)/( \sin(35) ) = (b)/( \sin(80) )`

`\rightarrow (8cm)/( 0.57 ) = (b)/( 0.98 )`

`\rightarrow 0.57b = 8cm * 0.98`

`\rightarrow 0.57b =7.84cm`

`\rightarrow b = (7.84cm)/(0.57) \\`

`\rightarrow b =13.8cm`

hence , Side AC = 13.8cm.

In ∆ ACD ,

Using the law of sines,

`\rightarrow (a)/( \sin(A) ) = (b)/( \sin(B) )`

where,

• a = x
• b = 13.8cm
• Sin(A) = Sin 75
• Sin(B) = Sin 60

`\rightarrow (x)/( \sin(75) ) = (13.8cm)/( \sin(60) ) \\`

`\rightarrow (x)/( 0.97) = (13.8cm)/( 0.87 ) \\`

`\rightarrow 0.87x = 13.8cm * 0.97`

`\rightarrow 0.87x = 13.39cm`

`\rightarrow x = (13.39cm)/(0.87) \\`

`\rightarrow x = 15.4cm`

Hence, the value of x would be equal to 15.4cm .