Solving Triangles

Solving Triangles: Level 2 Challenges


If the angles of a triangle are in the ratio \(4:1:1,\) then the ratio of the longest side to the perimeter is \(\text{__________}.\)

In the figure, \(\triangle ABC\) is an equilateral triangle where \(AB = 6\) cm. The area of the circumcircle is \(k\pi\) cm\(^{2}\). Find the value of \(k\).

If \(CD=\sqrt{3},\) \(PQ=2,\) and \(\angle PDQ=30^\circ,\) find \(CP.\)

In triangle \(ABC\), \( \angle BAC = 2 \angle ABC \), \( AB= 31, AC = 13 \). What is \(BC^2\)?

If \( AP = AC + 2\cdot CB \), what is the measure \(\angle ABP \) in degrees?


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