Call x and y those angles. If they are complementary, then their sum equals 90°:
x + y = 90°
y = 90° - x
The ratio of them is 5 to 1. So,
x/y = 5/1
x/(90° - x) = 5/1
x = 5 * (90° - x)
x = 450° - 5x
x + 5x = 450°
6x = 450°
x = 450°/6
x = 75°
The measure of the other angle is
y = 90° - 75°
y = 15°
The angles are 75° and 15°.
I hope it helps. =)
Answer:
Parallel
Step-by-step explanation:
Parallel lines have the same slope but different y-intercepts. If you multiply the top equation by 2, you get:
2(12x + 4y = 16)
24x + 8y = 32
This shows that both lines have the same slope, but then you find the y-intercepts, they are different:
1st equation y-int = 4
2nd equation y-int = 9/2 or 4.5
Drawing a diagram of a triangle may be helpful. The hypotenuse is irrelevant, but the vertical leg and the horizontal leg are useful. Since we know the engineer is looking up at a 45 degree angle from a distance of 200 feet, we can label the vertical leg the "opposite", since it is on the opposite side of the angle we are given. The horizontal leg then becomes the "adjacent". You can then use trigonometry to solve for the opposite.
The options are:
sin(theta)= opposite/hypotenuse
cos(theta)= adjacent/hypotenuse
tan(theta)= opposite/adjacent
Since we don't care about the hypotenuse, the last equation is the one to use. The angle we are given can be substituted in for theta:
tan(45)= x/200
1.61977519= x/200
x= 323.955038 feet
Raettttttrrrrrrrrrrrrrrrr
Answer:
79
Step-by-step explanation:
78
---------
7 | 62 03
49
----------
148 | 13 03
11 84
-----------
19
-----------
78^2 = 6084.
We observe that 78^2 < 6203.
79^2 = 6241.
We observe that 79^2 > 6203.
Hence the number to be added to 6203 is 6241 - 6203 = 38.
6203 + 38 = 3241
= 79 * 79
= 79.
Therefore 38 should be added to 6203 to obtain a perfect square.
