When we are given 3 sides, we try to solve the angles first by using the
law of cosines
cos (A) = [b^2 + c^2 - a^2] / (2 * b * c)
cos (A) = [43^2 + 17^2 -27^2] / (2 * 43 * 17)
cos (A) = [1,849 + 289 -729] /
<span>
<span>
<span>
1,462
</span></span></span>cos (A) = 1,409 / 1,462
cos (A) =
<span>
<span>
<span>
0.96374829001368
Angle A = 15.475
Now that we have one angle, we next can use the
Law of Sines
sin(B) / side b = sin(A) / side a
sin(B) = sin(A) * sideb / sidea
</span></span></span><span>sin(B) = sin(15.475) * 43 / 27
</span><span>sin(B) = 0.26682 * 43 / 27
sin (B) = </span><span>0.424935555555</span>
Angle B = 25.147 Degrees
Remember the arc sine (<span>0.424935555555) also equals </span>
<span>
<span>
<span>
154.85
</span></span></span>Finally, calculating the third angle is quite easy
Angle C = 180 - Angle (A) - Angle(B)
Angle C = 180 - 15.475 - 154.85
Angle C = 9.675
Source:
http://www.1728.org/trigtut2.htm
1/30 the explanation is joe
Answer:
-64
Step-by-step explanation:
5(x – 6) + 3x – 2
Distribute
5x - 30 +3x -2
Combine like terms
8x -32
Let x = -4
8*-4 -32
-32 -32
-64
If we imagine it in our head, we can see that the width (base) is 2 and the height is 9
the area is 1/2bh or 1/2*2=9 square units
it is rotated around x axis
meaning we have a sideways cone that is 2 hight and radius is 9
Vcone=1/3(hpir^2)
h=2
r=9
V=(1/3)(2)(3.141592)(9^2)
V=(2/3)(3.141592)(81)
V=(54)(3.141592)
V=169.6459
round
V=169.6 cubic units
base is 2 units
height is 9 units
area is 9 square units
it's a cone (sideways)
it has a volume of 169.6 cubic units
Answer:
- PS = 3
- SR = 3
- PQ = √29
- QR = √29
- kite
Step-by-step explanation:
A quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a <em>kite</em>.
Perhaps a more conventional definition of a kite is that it is a quadrilateral with two pairs of congruent adjacent sides.
<h3>1, 2)</h3>
The lengths PS and SR can be found by counting grid squares along the line segments. Each has a length of 3. They constitute one pair of congruent adjacent sides.
PS = SR = 3
__
<h3>3, 4)</h3>
The lengths of PQ an QR can be found using the distance formula. Essentially, it uses the Pythagorean theorem to compute the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates. For PQ and QR, those differences are 2 and 5, so the lengths of those segments are √(2² +5²) = √29.
PQ = QR = √29
__
<h3>5)</h3>
The figure has two pairs of congruent adjacent sides, so is a <em>kite</em>.
