From a window in room 7, one can observe the front door of Phillips Hall, which is about 45 yards away. A turn of the head trough an angle of 63 degrees in a counterclockwise direction enables one to see the front door to Jeremiah Smith Hall which is about 65 yds away. If you spot a friend coming out of that door and they proceed directly to Phillips Hall, making the trip in 48 seconds, what would you estimate to be your friend's average speed during the walk?

The 45 yd line represents the hor.

side of a rt. triangle. The 65 yd
line represents the hyp. of the rt.
triangle. The 63 deg. angle lies
between the hyp. and the 45 yd line.

Sin63 = d/65
d = 65 Sine 63 = 59.92 yds
d = r * t
r = d/t = 59.92/48 = 1.21 yds / sec.

CORRECTION:

d = 65 Sine 63 = 57.92 yds
r = d/t = 57.92/48 = 1.21 yds / sec.

After further analysis, I noticed that the conditions of the problem did not

create a rt. triangle. So I had to
redo the problem using the Law of Cosines. There is only a small difference in the results, but this
is the right procedure:

(Cos A = b^2 + c^2 - a^2) / 2bc.
(0.4540 = (45)^2 + (65)^2 - a^2) /
2 * 45 * 65,
Cross multiply:
(45)^2 + (65)^2 - a^2 = 0.454*2*45*65,
Solve for a:
6250 - a^2 = 2655.9
a = 59.95 yds. = Dist. traveled

d = r * t
r = d / t
r = 59.95 / 48 = 1.25 yds / sec.

To estimate your friend's average speed during the walk, we need to calculate the distance and the time taken. Let's break down the information provided:

1. Distance from Room 7 to the front door of Phillips Hall (Dph): 45 yards
2. Distance from Room 7 to the front door of Jeremiah Smith Hall (Djs): 65 yards
3. Time taken for the walk: 48 seconds

To determine your friend's average speed, we need to find the total distance traveled. Since your friend walked directly from Jeremiah Smith Hall to Phillips Hall, we can calculate the distance as the sum of the distances from Room 7 to each respective hall:

Total Distance (Dt) = Dph + Djs

Next, we'll calculate the average speed using the formula:

Average speed = Total Distance / Time taken

Let's substitute the values into the formula:

Average speed = (Dph + Djs) / 48 seconds

Now, calculate the total distance:

Dt = 45 yards + 65 yards
Dt = 110 yards

Finally, we can calculate the average speed:

Average speed = 110 yards / 48 seconds

Dividing these two values gives us the estimate.

Therefore, your friend's estimated average speed during the walk is approximately 2.29 yards per second.