Given that we have all three sides of the triangle, we can classify this as a Side-Side-Side (SSS) triangle. To find the angle, we start by applying the Law of Cosines specifically to the side opposite the angle of interest, which is angle W, opposite side XV:
XV² = XW² + WV² - 2(XW)(WV)cos W
Plugging in the known values:
116² = 96² + 89² - 2(96)(89)cos W
Calculating W
13,456 = 9,216 + 7,921 - 17,088 cos W
13,456 = 17,137 - 17,088 cos W
13,456 - 17,137 = 17,137 - 17,088 cos W - 17,137
-3,681 = -17,088 cos W
(-3,681)/(-17,088) = (-17,088 cos W)/(-17,088)
0.215414326 = cos W
cos W = 0.215414326
To find W:
W = cos^(-1)(0.215414326)
Calculating with a calculator:
W ≈ 77.56016397°
Rounded to one decimal place:
W ≈ 77.6°
Answer: The third option, 77.6°
Response:
Detailed explanation:
The timing data for each lap will form an arithmetic progression (AP) with a first term of 25 s and a common difference of 1.6 s.
a )
first term a = 25
common difference d = 1.6.
The 10th term of the sequence can be found using the formula
a₁₀ = 25 + (10-1) x 1.6
= 25 + 1.6 x 9
= 39.4 s
b )
Let n be the final lap
a(n) = a + (n-1) x d
55.4 = 25 + (n-1) x 1.6
n - 1 = 19
n = 20.
c )
The total for all terms in the AP
=(first term + last term) x number of terms / 2
= (25 + 55.4) x 20 / 2
= 804 s.
= 804 / 60 min
= 13.4 min.
