Find the length DE. Round your answer to the nearest tenth of a meter
1 answer:
You might be interested in
Answer:
The total distance Remy will swim is approximately 236 meters
Step-by-step explanation:
From the given diagram, of triangle ΔCAB, we have that the path Remy is to swim are;
1) Length of segment C to A
2) Length of segment A to B
3) Length of segment B to C
The length of the perpendicular at point D on segment AB to C = 60 meters
Therefore, DC = 60 m
By trigonometric ratios, we have;
We are given the values of the trigonometric ratios of the following angles;
tan(27°) = 0.51
tan(43°) = 0.93
cos(27°) = 0.89
cos(43°) = 0.73
∴ tan(43°) = AD/DC = 0.93
Where the lengths of AC, AD, DB, DC and BC
AD = DC × tan(43°)
∴ AD = 60 × 0.93 ≈ 55.8
Similarly, we have;
tan(27°) = DB/DC
∴ DB = DC × tan(27°)
DB = 60 × 0.51 ≈ 30.6
From , we have;
cos(43°) = DC/AC
AC = DC/(cos(43°))
∴ AC = 60/0.73 ≈ 82.2
Similarly, we have;
cos(27°) = DC/BC
BC = DC/(cos(27°))
∴ BC = 60/0.89 ≈ 67.4
The total distance Remy will swim = AC + AD + DB + BC
∴ The total distance Remy will swim = 82.2 + 55.8 + 30.6 + 67.4 = 236
The total distance Remy will swim = 236 meters