WILL MARK BRAINLIEST IF RIGHT
1 answer:
Answer:
- AB = 16√3
- AC = 8√3
- BC = 24
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
In ΔAHD, the side opposite angle DAH is DH, and the hypotenuse is AD, so we have ...
sin(∠DAH) = DH/AD = 4/8
∠DAH = arcsin(4/8) = 30°
That makes ΔAHD a 30°-60°-90° triangle, so the side lengths have the ratios 1 : √3 : 2.
∠CAB = 2·30° = 60°, so ΔABC is also a 30°-60°-90° triangle having the same ratios of side lengths.
In short, ...
AH = √3·DH = 4√3
AC = 2·AH = 8√3
AB = 2·AC = 16√3
BC = √3·AC = 8·(√3)² = 24
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