10th Grade Sine And Cosine Laws - Mixed (Nikoleta Simeonova)

Given a triangle ABC with sides 4 cm and 6 cm. The angles opposite them are in the ratio 1:2. Find the third side.

Given the inscribed quadrilateral ABCD, where AB=66cm, BC=77cm and AC=77cm. The angle bisectors of angles B and D intersect each other in point L, which lies on the diagonal AC. Find CD and AD.

Given a triangle ABC, such that a+c=11cm, c>a, β=60° and r= cm. Find a, b, c, .

Given the right angle triangle ABC. Points K and L lie on the hypotenuse AB, so that AK=KL=LB. Find cosβ, if CK=.CL.

Given a parallelogram ABCD (angle BAD is an acute angle). The orthogonal projection of AD over AC is 8 cm; the orthogonal projection of CD over AC is 16 cm; BD-=22 cm. Find the sides of ABCD.

Given a parallelogram ABCD, AB=13 cm, AD=16 cm, BN=9 cm (BN is the median in triangle ABD). Find the diagonals of ABCD.

A is exterior point for the circle k. AB is a tangent to k, ACD is a secant to k. AD-AB=24 cm. Find BC, if BD=56 cm and angle BAC is 60 degrees.

Given a triangle ABC with circumradius R. D lies on the short arc BC. The chords AD and BC intersect each other in point M, so that angle BMD is 120 degrees, BM:MC=2:3; AB=R. Find BC.

A circle k is inscribed in triangle ABC. The tangent point D divides AC into segments AD=6 cm, DC=4 cm. Find the sides AB and BC, if angle BAC is 60 degrees.

Given the rhombus ABCD. The side DC is seen from point M (the midpoint of AB) at angle 60 degrees. Find AC, if MD=4, MC=6.