Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on
land such that ÐCAB = 48.8°. He also measures CA as 318 ft and CB as 523 ft. Find the distance between A
and B. Please round the answer to the nearest tenth.
..pls help me this..
Sure, I can help you with that! To find the distance between points A and B, we can use the Law of Cosines. In this case, we have:
AC = 318 ft
CB = 523 ft
Angle CAB = 48.8°
The Law of Cosines formula states that:
c² = a² + b² - 2ab * cos(C)
Where c is the side opposite angle C, and a and b are the lengths of the other two sides.
Let's plug in the values into the formula. We want to find c, which is the distance between points A and B:
AB² = 318² + 523² - 2 * 318 * 523 * cos(48.8°)
Now we can solve for AB.
To find the distance between points A and B, you can use the Law of Cosines.
The Law of Cosines states that in a triangle, the square of one side (c) is equal to the sum of the squares of the other two sides (a and b), minus twice the product of the two sides (a and b) times the cosine of the included angle (C).
In this case, we can let side a be CA (318 ft), side b be CB (523 ft), and the included angle C be 48.8°.
Using the Law of Cosines, we can calculate the length of side c, which is the distance between points A and B:
c^2 = a^2 + b^2 - 2ab * cos(C)
Substituting in the given values:
c^2 = 318^2 + 523^2 - 2(318)(523) * cos(48.8°)
Solving for c, we get:
c ≈ sqrt(318^2 + 523^2 - 2(318)(523) * cos(48.8°))
c ≈ sqrt(101124 + 273229 - 330186 * cos(48.8°))
c ≈ sqrt(374353 - 330186 * cos(48.8°))
Using a calculator, we can find:
c ≈ sqrt(374353 - 330186 * 0.667091)
c ≈ sqrt(374353 - 219575.964)
c ≈ sqrt(154777.036)
c ≈ 393.4 ft (rounded to the nearest tenth)
Therefore, the distance between points A and B is approximately 393.4 ft.
To find the distance between points A and B, we can use the Law of Cosines.
The Law of Cosines states that for any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the included angle.
In this case, we know the lengths of sides CA (318 ft) and CB (523 ft), and the included angle CAB (48.8°). We can use the Law of Cosines to find the length of AB.
The formula for the Law of Cosines is:
c^2 = a^2 + b^2 - 2ab * cos(C)
where c is the side opposite the angle C, and a and b are the other two sides.
Let's plug in the values:
AB^2 = CA^2 + CB^2 - 2*CA*CB*cos(CAB)
AB^2 = 318^2 + 523^2 - 2*318*523*cos(48.8°)
Now, we can solve for AB:
AB = sqrt(318^2 + 523^2 - 2*318*523*cos(48.8°))
Calculating the above expression, we get:
AB ≈ 542.8 ft (rounded to the nearest tenth)
Therefore, the distance between points A and B is approximately 542.8 feet.
I assume you made the correct diagram.
First let's find angle B
sinB/318 = sin48.8/523
sinB = 318sin48.8/523
once you have angle B, we can find angle C
then using the sine law again
AB/sinC = 523/sin48.8
AB = 523sinC /sin48.5
I will leave the button pushing up to you
(I got 674.5)