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The questions below concern the following proof.

Let

$Delta ABC$ be an acute triangle. Let

$A$ represent

$m ang A$ ,

$B$ represent

$m ang B$ , and

$C$ represent

$m ang C$ . Prove the law of sines,

$(BC) / sin(A) = (AC) / sin(B) = (AB) / sin(C)$ .

Acute Triangle ABC v2

$" Statement "$	$" Reason "$
$1. "Construct altitude" \ \bar{BD} \ "such that" \ D \ "lies on" \ bar{AC}$	$1. ""$
$2. \bar{BD} _\|_ bar{AC}$	$2. "Definition of an altitude"$
$3. ang ADB, \ ang BDC " are right angles"$	$3. "Definition of perpendicular lines"$
$4. Delta ADB, \ Delta BDC " are right triangles"$	$4. "Definition of right triangles"$
$5.$	$5. "S""ine ratio in a right triangle"$
$6. AB sin(A) = BD$	$6. "Multiplication Property of Equality"$
$7.$	$7. "S""ine ratio in a right triangle"$
$8. BC sin(C) = BD$	$8. "Multiplication Property of Equality"$
$9. AB sin(A) = BC sin(C)$	$9. ""$
$10. AB = (BC sin(C))/sin(A)$	$10. "Division Property of Equality"$
$11. (AB)/sin(C) = (BC)/sin(A)$	$11. "Division Property of Equality"$
$12. "Construct altitude" \ \bar{AE} \ "such that" \ E \ "lies on" \ \bar[BC}$	$12. ""$
$13. \bar{AE} _\|_ \bar{BC}$	$13. "Definition of an altitude"$
$14. ang AEB, \ ang AEC " are right angles"$	$14. "Definition of perpendicular lines"$
$15. Delta AEB, \ Delta AEC " are right triangles"$	$15. "Definition of right triangles"$
$16.$	$16. "S""ine ratio in a right triangle"$
$17. AC sin(C) = AE$	$17. "Multiplication Property of Equality"$
$18.$	$18. "S""ine ratio in a right triangle"$
$19. AB sin(B) = AE$	$19. "Multiplication Property of Equality"$
$20.$	$20. "Transitive Property of Equality"$
$21. (AB sin(B))/sin(C) = AC$	$21. "Division Property of Equality"$
$22. (AB)/sin(C) = (AC)/sin(B)$	$22. "Division Property of Equality"$
$23. (BC)/sin(A) = (AC)/sin(B)$	$23. ""$
$24. (BC)/sin(A) = (AC)/sin(B) = (AB)/sin(C)$	$24. "Combined results"$

Grade 11 Trigonometry CCSS: HSG-SRT.D.10

The proof given applies to which type of triangles?

All triangles.
Acute triangles.
Non-right triangles.
Scalene triangles.

Question Info

Trigonometry Question

Grade 11 Trigonometry CCSS: HSG-SRT.D.10