Answer: The distance to the lodge is 1514 ft
Step-by-step explanation: Please refer to the diagram attached.
The point where Alexa is standing at the top of the hill is marked as point A. The vertical height of the hill is from point A to point B which has been given as 1209 ft. Also, when Alexa looks down, she does that at an angle of depression measuring 53 degrees. Therefore while looking at the lodge, she forms an angle between her line of sight and the height of the hill. That angle is calculated as 90 degrees minus 53 degrees and that equals 37 degrees (as shown in the diagram). Note that her line of sight is AC since the ski lodge is at point C. Therefore the distance she must ski in order to get to point C (which shall be represented by X) shall be calculated using trigonometric ratios.
Note that we have a reference angle which is 37. We also have an adjacent which is 1209 (the side that lies between the reference angle and the right angle). And then we want to calculate the hypotenuse, yet unknown, (which is the side facing right angle). Since we have an adjacent, a hypotenuse and the reference angle, X can be calculated as
Cos A = Adjacent/Hypotenuse
Cos A = AB/AC
Cos 37 = 1209/X
By cross multiplication we now have X = 1209/Cos 37
By using our calculator or checking the table of values, Cos 37 = 0.7986
X = 1209/0.7986
X = 1513.899
Approximated to the nearest feet,
X = 1514 ft
Answer:
A' (4,4), B' (5,7), C' (9,7)
Step-by-step explanation:
X = 59, y = 44
2x + 18 + x - 15 = 180
3x + 3 = 180
3x = 177
x = 59
x - 15 = y
59 - 15 = y
44 = y
Answer:
22.50
Step-by-step explanation:
0.75 x 30 years of mortgage
1. Need distance formula to find how long it is then cut it in half to find the radius....d= 10.....r= 5
Need midpoint formula to find the center....midpoint= (-1, -1)
(h,k) in the equation of a circle is the center, "r" is the radius. When you plug in the center, you have to put the opposite signs...so......
equation of a Circle = (x - h)^2 + (y - k)^2 = r^2 = (x + 1)^2 + (y + 1)^2= 25
2. A= pi(r^2)
200.96= 3.14(r^2)
64 = r^2
r = 8
Then to find the circumference, C= 2(pi)(r) = 2 (3.14) (8) = 50.24
For 3 and 4, is there a diagram?
A quilt design uses parallelogram-shaped pieces that have a base measure of 4 inches and a height of 6 inches. If 15 pieces are used in the quilt, what is the total area of the parallelogram-shaped pieces in the quilt?
1.225 in.
2.360 in.
3.(450 in.)
4.900 in.
<span> 15*4*6 = 360 sorry but I only have the answers for number 1 and 2
</span>