Pay attention here because I'm adding an extra letter to our circle to help keep track of the values in our formula. OUTSIDE of the intercepted arc I'm adding the point E. So the major arc is arc BEG and the minor arc is arc BG. The formula then for us is ∠
. We just don't have values for the arcs yet. If the measure of the central angle is 4x+238, then the measure of arcBG is also 4x+238. Around the outside of the circle is 360°. So we will use it in an expression. ArcBEG=360-(4x+238). Fitting that into our formula we have
![2x+146= \frac{1}{2}[(360-4x-238)-(4x+238)]](https://tex.z-dn.net/?f=2x%2B146%3D%20%5Cfrac%7B1%7D%7B2%7D%5B%28360-4x-238%29-%284x%2B238%29%5D%20)
. Doing all the simplifying inside there we have
and
. Multiply both sides by 2 to get rid of the fraction: 4x+292=-8x-116. Combine like terms to get 12x = -408 and divide to solve for x. x = -34. Fourth choice down from the top.
7.) Area of a square pyramid is given by A = s^2 + 2sl; where s is the side length of the base and l is the slant height.
Area of given pyramid = 4^2 + (2 x 4 x 7) = 16 + 56 = 72 ft^2
8.) Area of the given pyramid is the area of the hexagonal base plus the area of the six slant triangles.
Area of hexagonal base = (3sqrt(3))/2 x 10^2 = 150 x 1.732 = 259.8
Area of the 6 traingles = 6(1/2 x 10 x 13) = 6 x 65 = 390
Total surface area of the pyramid = 259.8 + 390 = 649.8 ≈ 650 m^2
9.) Using pythagoras rule, the slant height is sqrt(6^2 + 3.5^2) = sqrt(36 + 12.25) = sqrt(48.25) = 6.9 mm
10.) The surface area of a cone is given by πr^2 + πrl
Area = π x 6^2 + π x 6 x 20 = 36π + 120π = 490.1 cm^2
11.) l = sqrt(r^2 + h^2) = sqrt(11^2 + 16^2) = sqrt(121 + 256) = sqrt(377) = 19m
Answer:
9
Step-by-step explanation:
Answer:
Cos;
26 degrees
Step-by-step explanation:
Recall: SOH CAH TOA
Reference angle = y°
Adjacent side = 18 in.
Hypotenuse = 20 in.
We would apply the trigonometric function CAH since we are dealing with the Adjacent side (A) and the Hypotenuse (H). Thus:
Cos y° = Adj/Hyp
Cos y° = 18/20
Cos y° = 0.9
y° = cos^{-1}(0.9)
y = 25.8419328° ≈ 26 degrees (nearest whole degree)
The answers are:
Cos and 26 degrees
I would go for Obtuse from the 120° angle, Acute from the either the 20° and 40°, and scalene since all angles are unequal
