Victory for the ACT Student Text 15e

L ESSON 5 | T RIGONOMETRY • 247

TRIGONOMETRY AS AN ALTERNATIVE METHOD OF SOLUTION

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ O ‹• –Š‡…‡–‡” ‘ˆ –Š‡ …‹”…Ž‡ ™‹–Š ”ƒ†‹—• ͳͲǤ Šƒ– ‹• –Š‡ ƒ”‡ƒ ‘ˆ AOB T ǫ sin sin 30 2 1 60 2 3 ; c c e o

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ PQR T ƒ† QRS T ƒ”‡ ‹•‘•…‡Ž‡• ”‹‰Š– –”‹ƒ‰Ž‡•Ǥ ˆ QP 3 ǡ ™Šƒ– ‹• –Š‡ Ž‡‰–Š ‘ˆ QS ǫ sin4 2 2 5 c e o A. 2 B. 2 2 Ǥ Ͷ Ǥ ͸ Ǥ ͺ ˆ –Š‡ ƒ”‡ƒ ‘ˆ –Š‡ •“—ƒ”‡ JKLM ‹ –Š‡ ϐ‹‰—”‡ „‡Ž‘™ ‹• Ͷǡ ™Šƒ– ‹• –Š‡ •— ‘ˆ –Š‡ Ž‡‰–Š• ‘ˆ –Š‡ †‹ƒ‰‘ƒŽ• JL ƒ† KM ǫ sin45 2 2 c e o

9.

7.

Ǥ ͳͲ B. 10 3 Ǥ ʹͷ D. 25 3 Ǥ ͷͲ

8.

Š‡ –”‹ƒ‰Ž‡ ‹ –Š‡ ϐ‹‰—”‡ „‡Ž‘™ Šƒ• ƒ ƒ”‡ƒ ‘ˆ Ͷ͵Ͷ •“—ƒ”‡…‡–‹‡–‡”• ƒ† BC ‹• ͷͲ…Ǥ Šƒ– ‹• –Š‡ ˜ƒŽ—‡ ‘ˆ cos A ǫ F. 2 1 G. 2 2 Ǥ ͳ J. 2 K. 2 2 A C B 62 cm 15°

10.

F. 2 2 G. 2 2 2 H. 4 2 J. 4 4 2 K. 8 2