Question

4. Eratosthenes determined the earth's size in 240 B.C. While in Syene, Egypt (known today as Aswan), he noticed that the sun's rays shone directly down a well, casting no shac : w at all. From this, he concluded that the sun was directly overhead at Syene. On the same date in Alexandria, a one-meter rod perpendicular to the ground cast a shadow that was 0.125 m long. Assume that the distance between Syene and Alexandria is 805 kilometers. Determine the radius of the Earth according to Eratosthenes. 9. To find distance AB across a lake, a surveyor lays off length AC=50 m, so that the angle

C
is equal to 32
∘
and angle
B
is equal to 58
∘
. Determine the length AB.

Answer 1

the length AB across the lake is approximately 95.08 meters.

Step-by-step explanation:

To determine the length AB across the lake, we can use the law of sines. According to the law of sines, the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

In triangle ABC:

angle C = 32°

angle B = 58°

length AC = 50 m

Let's find angle A:

angle A = 180° - angle B - angle C

angle A = 180° - 58° - 32°

angle A = 90°

Now, we can use the law of sines:

AB / sin(A) = AC / sin(C)

Substituting the values:

AB / sin(90°) = 50 m / sin(32°)

Since sin(90°) = 1, the equation simplifies to:

AB = 50 m / sin(32°)

Let's calculate the length AB:

AB = 50 m / sin(32°)

AB ≈ 95.08 m

Therefore, the length AB across the lake is approximately 95.08 meters.