Cape Hatteras Lighthouse was built in 1870 and rises 208 feet above sea level. From the top of the lighthouse, the lighthouse ke
eper observes two ships along the same line of sight. The angle of depression to ship 1 is 20 and the angle of depression to ship 2 is 12.5 . For safety purposes, the keeper thinks the two ships should be at least 300 feet apart. If they are less than 300 feet apart, she will sound a warning. How far apart are the vessels? Will she sound the warning?
1 answer:
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Answer:
8.30256
Step-by-step explanation:
Step 1: Write out expression
Step 2: Use BPEMDAS to evaluate
= 8.30256
And we have our answer!
Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π and cos A = cos B · cos C
scratchwork:
A + B + C = π
A = π - (B + C)
cos A = cos [π - (B + C)] Apply cos
= - cos (B + C) Simplify
= -(cos B · cos C - sin B · sin C) Sum Identity
= sin B · sin C - cos B · cos C Simplify
cos B · cos C = sin B · sin C - cos B · cos C Substitution
2cos B · cos C = sin B · sin C Addition
Division
2 = tan B · tan C
<u>Proof LHS → RHS</u>
Given: A + B + C = π
Subtraction: A = π - (B + C)
Apply tan: tan A = tan(π - (B + C))
Simplify: = - tan (B + C)
Substitution: = -(tan B + tan C)/(1 - 2)
Simplify: = -(tan B + tan C)/-1
= tan B + tan C
LHS = RHS: tan B + tan C = tan B + tan C
