Precalculus Law of Sines and Law of Cosines Test with Point Values (PDF)
This laws sines cosines test for Precalculus covers law of sines and law of cosines (Common Core G-SRT.D.10, G-SRT.D.11, G-SRT.C.8), with a free PDF to print.
Time and points
- Grade: Precalculus
- Chapter: Law of Sines and Law of Cosines
- Standards: G-SRT.D.10, G-SRT.D.11, G-SRT.C.8
- Time: 45 minutes
- Total: 20 points
Laws sines cosines test: questions
Question 1 – Right triangle [2 pts]
A right triangle has an acute angle of \(28^{\circ}\) and an adjacent side of \(15\). Find the hypotenuse and the opposite side to the nearest hundredth.
Question 2 – Law of Sines [2 pts]
In triangle \(ABC\), \(A=45^{\circ}\), \(B=75^{\circ}\) and \(a=12\). Find \(b\) to the nearest hundredth.
Question 3 – Ambiguous case [2 pts]
(a) How many triangles have \(A=30^{\circ}\), \(a=4\), \(b=10\)? (b) For \(A=40^{\circ}\), \(a=8\), \(b=10\), find both possible values of \(B\).
Question 4 – Law of Cosines [2 pts]
Find \(c\) if \(a=6\), \(b=9\) and \(C=60^{\circ}\), to the nearest hundredth.
Question 5 – Find three angles [3 pts]
Find the angles \(A\), \(B\) and \(C\) of the triangle with \(a=8\), \(b=10\) and \(c=13\), to the nearest hundredth of a degree.
Question 6 – Area [2 pts]
Find the area of a triangle with sides \(7\) and \(10\) and included angle \(50^{\circ}\).
Question 7 – Heron's formula [2 pts]
Use Heron’s formula for the area of a triangle with sides \(9\), \(10\) and \(17\).
Question 8 – Hikers [3 pts]
Maya and Noah leave camp. Maya hikes \(4\) mi east. Noah hikes \(6\) mi in a direction \(50^{\circ}\) from Maya’s. (a) How far apart are they? (b) Find the area of the triangle formed. (c) Find the angle at Maya’s position.
Question 9 – Largest angle [2 pts]
Find the largest angle of a triangle with sides \(7\), \(9\) and \(12\) to the nearest hundredth.
Key facts behind this laws sines cosines test
- Law of Sines: a/sin A = b/sin B = c/sin C.
- Law of Cosines: c^2 = a^2 + b^2 – 2ab cos C.
- SSA can give 0, 1 or 2 triangles (the ambiguous case).
- Area = (1/2) a b sin C; Heron: sqrt(s(s – a)(s – b)(s – c)) with s = (a + b + c)/2.
- The angles of a triangle add to 180 degrees; the largest angle is opposite the longest side.
How to use this laws sines cosines test
Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.
All Precalculus chapters: Precalculus math.
