The hurdle and runner form a right triangle (see attached picture) such that
sin(30°) = <em>h</em> / (5 ft)
and
cos(30°) = <em>x</em> / (5 ft)
where <em>h</em> is the height of the hurdle and <em>x</em> is the horizontal distance from where the runner jumps to the hurdle. So
<em>h</em> = (5 ft) sin(30°) = 5/2 ft = 2.5 ft
<em>x</em> = (5 ft) cos(30°) = (5√3)/2 ft ≈ 4.33 ft
I don't have my calculator handy just now. But just looking at that problem, why don't you try +20 and -45 and see if they do the job.
Answer:
the solution is (-4, 2)
Step-by-step explanation:
6x + 8y = -8
x + 4y = 4
... can be solved using elimination by addition and subtraction, among other methods. Multiply the second equation by -2 to obtain
6x + 8y = -8
-2x - 8y = -8
Combining these results in
4x = -16. Thus, x = -4.
Substituting -4 for x in x + 4y = 4 results in
-4 + 4y = 4, or 4y = 8, or y = 2
Then the solution is (-4, 2)
We have a ratio of 3 hours / 7.5 miles
We want to know how many miles he can walk in 1 hour so, divide both sides by 3 -> 1 hour / 2.5 miles
He is walking at 2.5 mph
