Solving Triangles

Solving Triangles - Problem Solving


In triangle ABCABC, a=10a=10, b=11b=11 and c=12c=12. If cosA:cosC\cos A:\cos C can be expressed as an irreducible ratio m:nm:n, where mm and nn are positive integers, what is the value of m+nm+n?

Let ABCABC be a triangle and let aa, bb and cc be the lengths of the sides opposite to the vertices AA, BB and CC, respectively. If a3b+c=0 a - 3b + c = 0 and 2a+b2c=0 2a + b - 2c = 0 , the ratio sinA:sinB:sinC\sin A : \sin B : \sin C can be expressed as p:q:rp:q:r, where pp, qq and rr are coprime positive integers. What is the value of p+q+rp+q+r?

In a convex quadrilateral ABCD,ABCD, we are given the following three angles and side length: B=D=90,A=45,AC=32.\angle B=\angle D=90^\circ, \angle A=45^\circ, \lvert\overline{AC}\rvert= 3\sqrt{2}. What is the measure of the diagonal BD?\overline{BD} ?

Alice and Bob start walking at the same time from the same spot towards their respective directions, forming a 6060^\circ angle. Their speeds are 22m and 33m per second, respectively. If the distance between them 44 seconds after the start can be expressed as aba\sqrt{b}, where bb is prime number, what is a+ba+b?

In triangle ABCABC, B=30\angle B=30^{\circ}, C=90\angle C=90^{\circ}, and DD is a point on side BCBC such that BD=60\overline{BD}=60 and ADC=45\angle ADC=45^{\circ}. The length of side ACAC can be expressed as p(1+3)p(1+\sqrt{3}). What is the value of pp?


Problem Loading...

Note Loading...

Set Loading...