A triangular lot bounded by three streets has a length of 300 feet on one street, 250 feet on the second, and 420 feet on the th
ird. Find the measure of the largest angle formed by these streets. Which of the following equations can be used to solve the problem? 2502 = 3002 + 4202 - (2)(300)(420)cosx 3002 = 2502 + 4202 - (2)(250)(420)cosx 4202 = 3002 + 2502 - (2)(300)(250)cos
1 answer:
Answer:
420^2 = 300^2 + 250^2 - 2(300)(250)cosC
Step-by-step explanation:
a = 300
b= 250
c = 420
C= ??
Using Cosine rule
Cos C = (a^2 + b^2 - c^2) / 2ab
Cos C = (300^2 + 250^2 - 420^2) / 2*300*250
= (90000 + 62500 - 176400) / 150000
= -23900/150000
= -0.159
C = cos^-1(-0.159)
C = 80.85°
To find angle A
Cos A = (b^2 + c^2 - a^2) / 2bc
Cos A = (250^2 + 420^2 - 300^2) / 2*250*420
= (62500 + 176400 - 90000) / 210000
= 0.71
A = cos^-1(0.71)
A = 44.77°
A+B+C = 180°
B = 180 - (A+C)
B = 180 + (80.85 + 44.77)
B = 54.38°
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Answer:
The inequality to show how many hours of television Julia can still watch this week can be given as:
⇒
where represents he number of hours of television that Julia can still watch this week
On solving for , we get
Thus, Julia can still watch no more than 3.5 hours of television this week.
Step-by-step explanation:
Given:
Julia is allowed to watch television no more than 5 hours a week.
She has already watched 1.5 hours
To write and solve an inequality to show how many hours of television Julia can still watch this week.
Solution:
Let the number of hours of television that Julia can still watch this week be =
Number of hours already watched = 1.5
Total number of hours of watching television this week would be given as:
⇒
It is given that Julia is allowed to watch no more than 5 hours of television in a week.
Thus, the inequality can be given as:
⇒
Solving for
Subtracting both sides by 1.5
Thus, Julia can still watch no more than 3.5 hours of television this week.