Find the common denominator for 3 and 10 which is 30 now the denominator is 30 and what you do with one side you do to the other so 6 7/10 turns into
6 21/30 and 2 1/3 turns into 2 10/30 now subtract them so 6 21/30-2 10/30=
4 11/30
Answer:
69.01 m
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Tan = Opposite/Adjacent
The tangent function is useful for problems like this. Let the height of the spire be represented by h. The distance (d) across the plaza from the first surveyor satisfies the relation ...
tan(50°) = (h -1.65)/d
Rearranging to solve for d, we have ...
d = (h -1.65)/tan(50°)
The distance across the plaza from the second surveyor satisfies the relation ...
tan(30°) = (101.65 -h)/d
Rearranging this, we have ...
d = (101.65 -h)/tan(30°)
Equating these expressions for d, we can solve for h.
(h -1.65)/tan(50°) = (101.65 -h)/tan(30°)
h(1/tan(50°) +1/tan(30°)) = 101.65/tan(30°) +1.65/tan(50°)
We can divide by the coefficient of h and simplify to get ...
h = (101.65·tan(50°) +1.65·tan(30°))/(tan(30°) +tan(50°))
h ≈ 69.0148 ≈ 69.01 . . . . meters
The tip of the spire is 69.01 m above the plaza.
Volume of a cone = (π.R²)(h/3)
Diameter = 14cm then R=7 cm
Height = h= 2cm
Hence V=*π.7²)(2/3) ==> 98π/3 or 102.625 cm³