Law of Cosines

Grade 10·21 problems·~30 min·ACT Math·topic·act-geo-trig-lawcosines

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Recall / Warm-Up

In a right triangle with legs 5 and 12, what is the length of the hypotenuse?

169

What is the value of $\cos(60\degree)$ ?

0.5

$\frac{\sqrt{3}}{2}$

The three angles of a triangle always sum to:

$90\degree$

$180\degree$

$270\degree$

$360\degree$

In triangle $ABC$ , $a = 6$ , $b = 10$ , and $C = 60\degree$ . Find side $c$ . Round to the nearest tenth.

7.2

8.7

76.0

11.7

In triangle $PQR$ , $p = 8$ , $q = 5$ , and $R = 40\degree$ . Find side $r$ . Round to the nearest tenth.

In triangle $ABC$ , $a = 7$ , $b = 9$ , and $C = 120\degree$ . Find side $c$ . Round to the nearest tenth.

13.9

11.4

8.0

193.0

In triangle $ABC$ , $a = 5$ , $b = 8$ , and $c = 9$ . Find angle $C$ . Round to the nearest degree.

In triangle $DEF$ , $d = 11$ , $e = 7$ , and $f = 6$ . Find angle $D$ . Round to the nearest degree.

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