Question

Please help me solve this problem, it's a part of my homework and I'm just a bit stuck. thank you!

Answer 1

Given triangle is

Using the triangle sum property, we get

`\angle A+\angle B+\angle C=180^o`
`\text{ Substitute }\angle B=85^o\text{ and }\angle C=76^o,\text{ we get}`
`\angle A+85^o+76^o=180^o`

`\angle A=180^o-161^o`
`\angle A=19^o`

Given a=1200 yards.

We need to find b and c.

Consider the sine law.

`(\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)`

`\text{ Substitute }\angle A=19^o,\angle B=85^o\text{,}\angle C=76^o,\text{ and a=1200, we get}`

`(\sin 19^o)/(1200)=(\sin 85^o)/(b)=(\sin 76^o)/(c)`

`0.00027=(\sin85^o)/(b)=(\sin76^o)/(c)`

Consider the following equation to find the value of b.

`0.00027=(\sin85^o)/(b)`

`b=(\sin 85^o)/(0.00027)`
`b=3689.6\text{ yards.}`

Consider the following equation to find the value of c.

`0.00027=(\sin76^o)/(c)`

`c=(\sin 76^o)/(0.00027)`
`c=3593.7\text{ yards.}`

Hence the distances of the oil platform from each end of the beach are 3689.6 yards and 3592.7 yards.