You have to use the Law of Cosines here, since there's no other way to solve this. it's not a right triangle, so you can't use the Pythagorean Theorem. The Law of Cosines will help us find the missing side length then we will have to use the Law of Sines to find another angle. Then after that we will use the Triangle Angle-Sum theorem to finish it off. Ready? The Law of Cosines to find side b is
and fill in the info we know, which is everything but the b. 
. Doing all that math gives us that side b = 40.9 or 41. Now the Law of Sines to find missing angle A or C. Let's find A. 
. That gives us that angle A is 29. Now use the fact that all triangles add up to 180 to get that angle C is 42. And you're done!
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1 answer:
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Answer:
Step-by-step explanation:
<u><em>The correct question is</em></u>
Which equation represents a parabola that opens upward, has a minimum value of y=3, and has an axis of symmetry at x= 3?
<em>Verify each case</em>
case 1) we have
This a vertical parabola open upward (the leading coefficient is positive)---> is ok
The vertex represent a minimum ---> is ok
The vertex is the point (-3,-6)
The minimum value of y=-6 ----> is not ok
The axis of symmetry is x=-3 ----> is not ok
case 2) we have
This a vertical parabola open upward (the leading coefficient is positive)---> is ok
The vertex represent a minimum ---> is ok
The vertex is the point (-3,3)
The minimum value of y=3 ----> is ok
The axis of symmetry is x=-3 ----> is not ok
case 3) we have
This a vertical parabola open upward (the leading coefficient is positive)---> is ok
The vertex represent a minimum ---> is ok
The vertex is the point (3,-6)
The minimum value of y=-6 ----> is not ok
The axis of symmetry is x=3 ----> is ok
case 4) we have
This a vertical parabola open upward (the leading coefficient is positive)---> is ok
The vertex represent a minimum ---> is ok
The vertex is the point (3,3)
The minimum value of y=3 ----> is ok
The axis of symmetry is x=3 ----> is ok
Answer:
Height of mound = 794 ft
Step-by-step explanation:
To illustrate the angle of elevation and distance, i have drawn it and attached below.
Now, from my diagram;
h = the height of the mound
At his first point of his trip to the foot of the mound, the angle of elevation is 40°, while the horizontal distance to the foot of the mound is "X"
So, by triangle definition,
tan(40°) = h/x
And so;
h = x tan40
h = 0.8391x - - - - (eq 1)
At his second point of the trip to the foot of the mound, Joe is now,
"(x - 450) ft" from the foot of the mound.
Thus, his angle of elevation is 40 + 18 = 58°.
So, by triangle definition,
tan(58°) = h/(x - 450)
h = (x - 450)•(tan(58°))
h = 1.6003(x - 450)
h = 1.6003x - 720.135 - - - - -(eq2)
To get the height(h) of the mound, let's equate (eq1) to (eq2).
0.8391x = 1.6003x - 720.135
1.6003x - 0.8391x = 720.135
0.7612x = 720.135
x = 720.135/0.7612
x = 946.0523 ft
Let's put this value for x in eq (1);
h = 0.8391 x 946.0523 = 793.83 ft ≈ 794ft
