# Cos/Sin Rule Exercises: Challenges and Solutions

• Rukawa0320

#### Rukawa0320

Hey guys,

We've been learning cos/sin rule since the 1st of school, and i really had difficulties with the following exercises, I've been working them yesterday for 2-3 hours and could only manage to do part of it...

1. IN Quadrilateral ABCD, AB=7 cm, BC= 8cm, CD=5cm and angle ABC=52. Given that ABCD is a cyclic quadrilateral, find the radius of its circumscribing circle and the length of AD.

I was able to calculate the AD, which is about 2,26cm and i also got that the diameters of the quadrilateral are 8cm and 6,63cm. I tried to apply Thales's theorem in the circle, but couldn't really find a solution.

2. From a barge moving with constant speed along a straight canal the angle of elevation of a bridge is 10 degrees. After 10 minutes the angle is 15 degrees. How much longer will it be b4 the barge reaches the bridge, to the nearest second.

3. A tower stand on a slope which is inclined at an angle of 17,2 degrees to the horizontal. From a point further up the slope and 150m from the base of the tower the angle of depresssion of the top of the tower is found to be 9.6 degrees. Find the height of the tower.

I started doing 2 and 3, but couldn't get the idea how to solve it properly, of course i got some extra datas but coundt use it to solve the problem.

Any help appreciated