Standard +0.8 This is an ambiguous case sine rule problem requiring students to recognize that two triangles ABD are possible, apply the sine rule to find angle ADB, and identify both solutions. The setup is non-standard (point D on AC with given BD length) requiring careful geometric reasoning and awareness that sin θ = sin(180° - θ), making it moderately challenging but within typical A-level scope.
7. In the triangle \(A B C\), the length \(A B = 6 \mathrm {~cm}\), the length \(A C = 15 \mathrm {~cm}\) and the angle \(B A C = 30 ^ { \circ }\).
\(D\) is the point on \(A C\) such that the length \(B D = 4 \mathrm {~cm}\).
Calculate the possible values of the angle \(A D B\). [0pt]
7. In the triangle $A B C$, the length $A B = 6 \mathrm {~cm}$, the length $A C = 15 \mathrm {~cm}$ and the angle $B A C = 30 ^ { \circ }$.\\
$D$ is the point on $A C$ such that the length $B D = 4 \mathrm {~cm}$.\\
Calculate the possible values of the angle $A D B$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2024 Q7 [3]}}