help with these math questions please!!?

hi everyone.. so i really need this help for math (i have an exam tomorrow and i need to know how to do this because i have no clue )
ps this symbol ⁰ means degrees lol
so one question is:
8. While sailing, Mark notices a point of land at an angle of 52⁰ to the right of his direction of travel. After moving forward in a relatively straight path for 0.85 km, the same point of land is at an angle of 82⁰ to the right of the direction of travel.
a) how far is mark from the point of land?
b) how close to the point of land will his current path take him?

8
Let’s put some marks (oopppsss). The point he was when he saw the island at 52 degrees is C. The point he was when he saw the island at 82 degrees is A and the island is at the point B. You get it ?

a) how far is mark from the point of land?

Those three points makes a triangle and the only way to solve it is with the law of sines :
sin(A) / BC = sin(B) / AC = sin(C) / AB
angle A is 180 – 82 = 98 degrees
angle C is 52 degrees (given)
angle B is 180 – 98 – 52 = 30 degrees

AC = 0.85 km (given)

We are searching for AB so we will use only :
sin(B) / AC = sin(C) / AB
AB = sin(C) * AC / sin(B)
AB = sin(52) * 0.85 / sin(30)
AB = 1.34 km.

b) how close to the point of land will his current path take him?
It is when he will see the island at an angle of 90 degrees. Let’s name that point D. We have a new triangle DAB which is a right triangle.
Angle D = 90 degrees
Angle A = 82 degrees (given)
Angle B = 180 – 90 – 82 = 8 degrees
AB = 1.34

We are searching for DB. Again with the law of sines :
sin(D) / AB = sin(A) / DB
DB = sin(A) * AB / sin(D)
DB = sin(82) * 1.34 / sin(90)
DB = 1.327 km.

#2
I don’t understand the question. You can post your picture at www.photobucket.com if you have a chance to scan it.

titandude21- Mario Golf Toadstool Tour Hole-in-ones

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