Law of Sines Assignment and Quiz

What is the approximate length of KL? Use the law of sines to find the answer.

3.2 units

What is the value of z, rounded to the nearest tenth? Use the law of sines to find the answer.

3.2 units

Use the law of sines to find the value of w. (VUW, 31°, 39°, 3.3cm) What is the best approximation of the value of w?

4.0 cm

What is the approximate measure of angle F? Use the law of sines to find the answer.

44.4°

In △FGH, h = 10, m∠F = 65°, and m∠G = 35°. What is the length of g? Use the law of sines to find the answer.

5.8 units

What is the measure of angle E? m∠E = __° What is the length of EF rounded to the nearest hundredth? EF ≈ ____

55 12.49

What is the approximate perimeter of the triangle? Use the law of sines to find the answer.

9.2 units

Ivan began to prove the law of sines using the diagram and equations below. sin(A) = h/b, so b sin(A) = h. sin(B) = h/a, so a sin(B) = h. Therefore, b sin(A) = a sin(B). Which equation is equivalent to the equation b sin(A) = a sin(B)?

B

When using the law of sines, why can the SSA case result in zero, one, or two triangles? Explain.

If you have SSA, then the third side determines the triangle. If it is too short to intersect the other side, then it does not form a triangle. The third side can also be just the right length to meet the other side, making one triangle. Finally, the third side might be long enough to intersect the other side at two different points, creating two triangles. When the third side of the triangle is too short to intersect the other side, no triangles can be formed. When the third side is just long enough to meet the other side at one point, one triangle is formed. When the third side is long enough to intersect the other side at two points, two triangles are formed.

In △MNO, m = 20, n = 14, and m∠M = 51°. How many distinct triangles can be formed given these measurements?

There is only one distinct triangle possible, with m∠N ≈ 33°.

A surveyor found the angle of elevation from the ground to the top of the building at two locations 20 feet apart as shown below. Which measurements are correct? Round side lengths to the nearest hundredth. Check all that apply.

m∠B = 15° h ≈ 31.28 ft

Determine the measures of all unknown angles and side lengths of ΔPQR. Round side lengths to the nearest hundredth.

m∠R = 50° PR ≈ 5.74 PQ ≈ 8.53

Which equation is true for triangle QRS?

sin(100°)/3.5 = sin(S)/2.4

Use the law of sines to find the value of y. Round to the nearest tenth.

y = 2.5

Which expression represents the approximate length of BC?

(3)sin(66°)/sin(38°)

How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10? How many distinct triangles can be formed for which m∠J = 129°, k = 8, and j = 3?

1 triangle 0 triangle

Ships A and B are 1,425 feet apart and detect a submarine below them. The angle of depression from ship A to the submarine is 59°, and the angle of depression from ship B to the submarine is 47°. How far away is the submarine from the two ships? Round to the nearest hundredth of a foot. The distance from ship A to the submarine is about ________ feet. The distance from ship B to the submarine is about ________ feet.

1048.18 1270.69

In ΔABC, c = 5.4, a = 3.3, and A = 20°. What are the possible approximate lengths of b? Use the law of sines to find the answer.

2.3 units and 7.8 units

Which expression gives the exact value of t?

21.3sin(34°)/sin(118°)