Mastery Test on Trigonometry: Right & Oblique Triangle Application
Pitogo High School
Pre-calculus
2nd QT Mastery Test #1
Name: _____________________________________________ Date: _________________
Yr.&Sec.: _____________________________________________ Teacher: _________________
Direction: Read the following then answer correctly. Write your answer & solutions on a separate answer sheet.
A. True or False.
______1. The area of a triangle equals one-half the product of two of its side lengths and the sine of the angle.
______2. Given only the three sides of a triangle, there is insufficient information to solve the triangle.
______3. Given two sides and the included angle, the first thing to do to solve the triangle is to use the Law of Sines.
______4. The Law of Sines states that the ratio of the sine of an angle in a triangle to its opposite side is equal to the ratios of the sines of the other two angles to their opposite sides.
______5. Law of Cosines says that the square of any side of a triangle is equal to the squares of the sum of the other two sides, minus twice the product of those two sides times the cosine of the included angle.
______6. If you are given the lengths of two sides of a right triangle, you can solve the right triangle.
______7. If you are given the length of the hypotenuse of a right triangle and the measures of the angle opposite the hypotenuse, you can solve the right triangle.
______8. The semiperimeter of any triangle is one-half the sum of its angles.
______9. A businessman wishes to buy a triangular lot in a busy downtown location. If the lot frontages on the three adjacent streets are 125, 280, and 315 ft., then area of the lot is 17, 452 ft.
______10. The Law of Sines can be used in triangles given one side and two angles.
B. Solve for x.
1. 2. 3.
4. 5.
C. Solve the following problems.
1. A 96-ft tree casts a shadow that is 120 ft long. What is the angle of elevation of the sun?
2. A 20-ft ladder
Pre-calculus
2nd QT Mastery Test #1
Name: _____________________________________________ Date: _________________
Yr.&Sec.: _____________________________________________ Teacher: _________________
Direction: Read the following then answer correctly. Write your answer & solutions on a separate answer sheet.
A. True or False.
______1. The area of a triangle equals one-half the product of two of its side lengths and the sine of the angle.
______2. Given only the three sides of a triangle, there is insufficient information to solve the triangle.
______3. Given two sides and the included angle, the first thing to do to solve the triangle is to use the Law of Sines.
______4. The Law of Sines states that the ratio of the sine of an angle in a triangle to its opposite side is equal to the ratios of the sines of the other two angles to their opposite sides.
______5. Law of Cosines says that the square of any side of a triangle is equal to the squares of the sum of the other two sides, minus twice the product of those two sides times the cosine of the included angle.
______6. If you are given the lengths of two sides of a right triangle, you can solve the right triangle.
______7. If you are given the length of the hypotenuse of a right triangle and the measures of the angle opposite the hypotenuse, you can solve the right triangle.
______8. The semiperimeter of any triangle is one-half the sum of its angles.
______9. A businessman wishes to buy a triangular lot in a busy downtown location. If the lot frontages on the three adjacent streets are 125, 280, and 315 ft., then area of the lot is 17, 452 ft.
______10. The Law of Sines can be used in triangles given one side and two angles.
B. Solve for x.
1. 2. 3.
4. 5.
C. Solve the following problems.
1. A 96-ft tree casts a shadow that is 120 ft long. What is the angle of elevation of the sun?
2. A 20-ft ladder