can anyone help me answer the questions i tried 3 times but i keep getting 558

Question

Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such than ∠CAB=49.5°∠���=49.5°. Find the distance across the lake from A to B.

365 yd502 ydCBA49.5°[Graphs generated by this script: setBorder(0); initPicture(-5,5,-3,4); text([0,-2.5], "365 yd"); text([-2,1], "502 yd"); text([-4.3,-2.3], "C"); text([1,3.3], "B"); text([4.3,-2.3], "A"); text([2.7,-1.2],"49.5°"); stroke = "blue"; st

distance =  yd

Answer 1

You have three points, uppercase A, B, C, which are the vertices of a triangle.

As usual, the length of side AB is called lowercase c, the length of side BC is called a,

and the length of side AC is called b.

We want to find the length of side AB (also known as c).

Draw a picture of the above triangle.

You said that angle CAB is 49.5°. You also said that angle CBA is 49.5°.

I believe you mean to say that angle ACB (also known simply as angle C) is 49.5°.

Write the 49.5° at angle C of the triangle.

I believe you mean to say that the length of side AC (also known as b) is 365 yards.

I believe you mean to say thatthe length of side BC (also known as a) is 502 yards.

Write these numbers along sides b and a.

Now, to find the length of side AB (also known as c), use the Law of Cosines:

c² = a² + b² - 2 ab cos c.

Substituting in the numbers we were given,

c² = 365² + 502² - 2 times 365 times 502 times cos 49.5°

Doing the arithmetic,

c² = 133225 + 252004 - 366460 times 0.64944

c² = 385229 - 237993.7824

c² = 147235.2176

Taking square roots on both sides,

c = 383.7124 yards is the distance from A to B.

If triangle ABC had been a right triangle, we could have used the Pythagorean theorem c² = a² + b² to get the length of side AB (also known as c). But it's not a right triangle, so we had to resort to the similar but more complicated Law of Cosines. Good luck.

Answer 2

∠A = 49.5

I'm assuming:

a=502

b=365

Distance from point A and point B = c

Using cosine law:

a² = b²+c²-2bcCos(A)

502²=365²+c²-474.1c

c²-474.1c-118779=0

c=655.346, -181.246

Distance from A to B = 655.346 yds