Properties of Triangles — Engineering Board Exam Practice Questions

17 free engineering board exam reviewer questions on Properties of Triangles (Trigonometry), each with the correct answer and a worked solution.

  1. ECE Board November 1998: Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of…
  2. EE Board October 1997: The sides of a triangle are 195, 157 and 210, respectively. What is the area of the triangle?
  3. ECE Board April 1998: The sides of a triangle are 8, 15 and 17 units. If each side is doubled, how many square units will the area of the…
  4. A right triangle has legs 20 and 21 and hypotenuse 29. Find the distance between its incenter and circumcenter.
  5. The three altitudes of a triangle are 12, 15 and 20 units long. Find the area of the triangle.
  6. In triangle ABC, BC=14, CA=15 and AB=13. Find the distance from vertex A to the incenter.
  7. Find the area of a triangle with sides 9, 10 and 17.
  8. A triangle is inscribed in a circle of radius 10. Find the side opposite an angle of 30°.
  9. For the triangle with sides a=13, b=14 and c=15, find the exradius opposite side a.
  10. Find the radius of the inscribed circle of a right triangle with legs 6 and 8.
  11. In triangle ABC, BC=6, CA=9 and AB=10. The bisector of angle C meets AB at D. Find the length of DB.
  12. Find the altitude to the longest side of the triangle with sides 13, 14 and 15.
  13. In the triangle with sides 13, 14 and 15, find the length of the median drawn to the side of length 14.
  14. Find the radius of the circumscribed circle of the triangle with sides 13, 14 and 15.
  15. Find the radius of the inscribed circle of the triangle with sides 13, 14 and 15.
  16. Find the area of an equilateral triangle whose side is 10.
  17. Find the area of a triangle with sides 5, 6 and 7.