Question

83
Find A B
у
2
ROY
Зо°
9.ro
시
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Answer 1

Answer:

• tan 30=80/AC
• AC × 1/root 3=80
• AC=80×root 3

• tan 45=80/BC
• BC × 1=80
• Bc=80

• AB=AC-BC
• AB=80(root 3-1)

Answer 2

Answer:

$AB = 80( \sqrt{3} - 1)m$

Step-by-step explanation:

$In \: ΔBCD, \\ tan \: 45= \frac{CD}{BC} \\ 1 = \frac{80}{BC} \\ BC = 80m \\ In \: ΔACD, \\ tan \: 30 = \frac{CD}{AC} \\ \frac{1}{ \sqrt{3} } = \frac{CD}{</p><p>AB+BC} \\ \frac{1}{ \sqrt{3} } = \frac{80}{AB + 80} \\ Cross \: multiply \\ AB + 80 = 80 \sqrt{3} \\ AB = 80 \sqrt{3} - 80 \\ AB = 80( \sqrt{3} - 1)m$