Trig Help: installing sprinkler at point B on triangle....

[kaytee16]

The vertices of the triangle are A(15,40), B(-30,-20) and C(60,10).
Jack was installing a sprinkler at point B and he noticed that it had a maximum left/right arc odf35 degrees. Use trigonometry to determine if this arc will be enough to water all the crops in this corner of the field.

The height and distance of the sprinkler follows the quadratic relation h=-0.1d^2 +1.6d+3.6, where h is the height of the water, and d is the distance from the spout, both in meters.

a) Use the zeros to determine the horizontal distance that the water will reach.

b)What is the maximum height reached by the sprinkler?

 

[tkhunny]

What's your plan for solving these?

Have you the Law of Cosines? You need that angle at B. There are various ways to go about it. What section's methods should you be using?

h=-0.1d^2 +1.6d+3.6

Well, use the zeros! 0=-0.1d^2 +1.6d+3.6 -- Solve for 'd'.

What do you know about Quadratics? Parabolas? Where is the maximum attained? Is there a maximum? How do you know?

Please show some work. Don't make us pull it out of you.

 

[kaytee16]

yes, i should be using cosine law, but i dont really know anything else:$ im horrible at math

 

[tkhunny]

im horrible at math

Never say that again.

Maybe it's new territory. That's why we call it learning.

At least you didn't pick a silly screen name like "imhorribleatmath". This encourages me.

One step at a time. No need to panic because you can't see the end from the beginning.

1) You also need the Distance Formula on this one.
2) Use the distance Formula to calculate the length of each of the three sides of the triangle.
3) Give the Law of Cosines another look and see if it makes any sense to you.