Answer:
yes ; 17.5 ft
Step-by-step explanation:
Triangle PRQ is isosceles
the base angle are equals
we know two legs, so we can find the tangent of angle x
tan = opposite/adjacent
tan = 7/16 = 0.4375
the angle x measure 23.6 degrees circa (we can calculate this with the button tan -1 on the calculator)
the roof is safe
B we can use the Phytagorean theorem to solve this
PR = √16^2 + 7^2 = √256 + 49 = 17,46... = 17.5 ft
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.
Answer:
j = 21 and n = 14
Step-by-step explanation:
we have the equations:
6j + n/3 = 134
j/3 + n = 31
54j + 3n = 1206
j + 3n = 93
53j = 1113
j = 21
(21)/3 + n = 31
7 + n = 31
n = 14
Answer:
( x - 2 ) ( x + 2 ) ( x² + 4 ) - ( x² - 2 ) ( x² + 3 )
(x²– 4) (x²+4) – (x⁴ + x² – 6)
( x⁴ – 16 ) – ( x⁴ + x² – 6 )
( x⁴ – 16 ) + ( – x⁴ – x² + 6 )
– x² – 10
I hope I helped you^_^