(i.) CA = πrl
CA = π (5*13)
CA = 65π
(ii.) TA = πrl + πr^2
TA = 65π + π (5^2)
TA = 65π + 25π
TA = 90π
(iii.) To get the height of the cone, you have to use the Pythagorean theorem. Plug in the radius for a and the slant height for c.
a^2 + b^2 = c^2
5^2 + b^2 = 13^2
25 + b^2 = 169 Height = 12
b^2 = 144
b = 12
(iv.) v = (1/3)πr^2h
v = (1/3)π(5^2)*12
v = (1/3)π(25*12)
v = (1/3)π*300
v = 100π
Yes, that is the famous first Pythagorean triplet: 3²+4²=5²
or
For three lengths to be able to form a triangle, it suffices that every one of those lengths is shorter than the sum and longer than the difference of the other two.
It is enough to check just one side.
So,
3 + 4 > 5
4 - 3 < 5
Your triangle is constructible.
Answer:
135° and 225°
Step-by-step explanation:
basically you want to find the value of x between 0 and 360 in this equation
cos x/2 = -(√2)/2
assume x/2 as n, so
cos n = -(√2)/2
n = 45°
then remember the quadrant system
0-90 1st quadrant, all is POSITIVE
90-180 2nd quadrant, only SIN has positive value
180 - 270 3rd quadrant, only TAN has positive value
270 -360 4th quadrant, only COS positive here.
so if you try to find negative value look into 2nd and 3rd quadrant that related 45° to x-axis (0°or 180°)
so the value of x is
180 - 45 = 135° (2nd quadrant) and
180 + 45° = 225° (3rd quadrant)
PNL and VNM; PNM and LNV. THis is because vertical angles are always congruent.
Hope this helps!
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