Task Sets: Apply Law of Sines and Cosines - Common Core Math - HS Geometry

$Triangle ABC with angle A = 35 degrees, angle B = 85 degrees, and side a = 10, with side b to be found$

1.

In triangle $ABC$ , angle $A = 35\degree$ , angle $B = 85\degree$ , and side $a = 10$ . Use $\sin(35\degree) \approx 0.574$ and $\sin(85\degree) \approx 0.996$ . Find side $b$ . Round to the nearest tenth.

2.

In triangle $ABC$ , angle $A = 50\degree$ , angle $C = 70\degree$ , and side $c = 20$ . Use $\sin(50\degree) \approx 0.766$ and $\sin(70\degree) \approx 0.940$ . Find side $a$ . Round to the nearest tenth.

3.

In triangle $ABC$ , angle $A = 30\degree$ , side $a = 8$ , and side $b = 12$ . Compute $\sin B = \dfrac{b \sin A}{a} = \dfrac{12 \times 0.5}{8} = 0.75$ . How many valid triangles exist with these measurements?

A.

No valid triangles — $\sin B > 1$

B.

Exactly one triangle — the acute triangle only

C.

Exactly two triangles — $B \approx 48.6\degree$ or $B \approx 131.4\degree$

D.

Exactly one triangle — the obtuse triangle only

$Triangle ABC with sides a = 8 and b = 11 and included angle C = 50 degrees, with side c to be found$

4.

In triangle $ABC$ , side $a = 8$ , side $b = 11$ , and angle $C = 50\degree$ . Use $\cos(50\degree) \approx 0.643$ . Find side $c$ . Round to the nearest tenth.

5.

In triangle $ABC$ , all three sides are known: $a = 5$ , $b = 7$ , $c = 9$ . Use the Law of Cosines to find angle $C$ (the largest angle, opposite side $c$ ). Use $\cos^{-1}(-0.100) \approx 95.7\degree$ . Round to the nearest tenth of a degree.

Exercises: Apply the Law of Sines and the Law of Cosines

Recall / Warm-Up

Fluency Practice