SinA/sinB=2/√3 and cosA/cosB=1/√2 ,tan^2B=?
1 answer:
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Answer:
Step-by-step explanation:
This is one of the more interesting motion problems I've seen. I like it! If Kelly is driving north (straight up) for 9 miles, then turns east (right) and drives for 12 miles, what we have there are 2 sides of a right triangle. The hypotenuse is created by Brenda's trip, which originated from the same starting point as Kelly and went straight to the destination, no turns. We need the distance formula to solve this problem, so that means we need to find the distance that Brenda drove. Using Pythagorean's Theorem:
and
and
so
c = 15.
Brenda drove 15 miles. Now we can fill in a table with the info:
d = r x t
Kelly 12+9 42 t
Brenda 15 45 t
Because they both left at the same time, t represents that same time, whatever that time is. That's our unknown.
If d = rt, then for Kelly:
21 = 42t
For Brenda
15 = 45t
Solve Kelly's equation for t to get
t = 1/2 hr or 30 minutes
Solve Brenda's equations for t to get
t = 1/3 hr or 20 minutes
That means that Brenda arrived at the destination 10 minutes sooner than Kelly.