1. 
In triangle ABC, the ratio of the measure of angle A to angle B is 1:3. The measure of angle C is half the sum of the measures of angles A and B. If AC = 12, find BC. 

2. 
If BC = 35, find CD.



4. 
In right _{}ABC, _{} is the altitude to hypotenuse _{}. If DB = 5 and AD = 7, find CD. 


6. 
_{}ABC is a right isosceles triangle with C at the right angle. If BC = 5x  263 and AC = x  35, find the perimeter of the triangle. 

7. 
Cable is needed to support a 18foot vertical pole. The angle between the pole and the cable is to be 30 degrees. Find the length of the cable. 

8. 
The bases of isosceles trapezoid ABCD are 21 cm and 29 cm and its base angles (angles A and B) are 45 degrees. What is the height of the trapezoid? 

9. 
In _{}ABC, m_{}A = 30 and m_{}C = 90. If the length of BC is seven more than onefourth of AB, find the length of the longer leg of the triangle. 

10. 
A right triangle is inscribed in a circle with radius 9. What is the perimeter of the triangle if the length of the hypotenuse is twice as long as the shorter leg? 
