Trigonometry Question

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Let

$Delta ABC$ be an obtuse triangle, where

$m ang BAC > 90°$ . Let the intersection of the altitude from vertex

$B$ and the extension of side

$\bar{AC}$ be point

$D$ (not labeled), such that

$AD + AC = CD$ . Let

$m ang BAC = theta$ and

$m ang BAD = alpha$ . Derive the sine formula for the area of a triangle,

$A_{Delta ABC} = 1/2 AC \ AB sin(theta)$ .

Obtuse Triangle Height v2

$" Statement "$	$" Reason "$
$1. bar{BD} " is an alitutde"$	$1. "Given"$
$2. A_{Delta ABC} = 1/2 AC \ BD$	$2. "Standard formula for area of a triangle"$
$3. alpha + theta = 180°$	$3. ""$
$4. alpha = 180° - theta$	$4. "Subtraction Property of Equality"$
$5. bar{BD} " is an alitutde"$	$5. "Previous result"$
$6. bar{BD} _\|_ bar{AD}$	$6. ""$
$7. ang ADB " is a right angle"$	$7. "Definition of perpendicular lines"$
$8. Delta ADB " is a right triangle"$	$8. "Definition of a right triangle"$
$9.$	$9. "S""ine ratio in a right triangle"$
$10. sin(180°-theta) = (BD)/(AB)$	$10. "Substitution Property of Equality"$
$11. sin(theta) = (BD)/(AB)$	$11. "Trig Identity"$
$12. AB sin(theta) = BD$	$12. "Multiplication Property of Equality"$
$13. A_{Delta ABC} = 1/2 AC \ AB sin(theta)$	$13. ""$

Grade 11 Trigonometry CCSS: HSG-SRT.D.9

What is the missing reason in step 6?

Definition of an altitude
Perpendicular Bisector Theorem
Triangle Bisector Theorem
$bar{AC}$ and $bar{CD}$ are not parallel so they must be perpendicular

Question Info

Trigonometry Question

Grade 11 Trigonometry CCSS: HSG-SRT.D.9