Answer:
407.22 foot is the boat from the base of the lighthouse
Step-by-step explanation:
Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.
Let x foot be the distance of the object(boat) from the base of the lighthouse
Angle of depression = ![7^{\circ}](https://tex.z-dn.net/?f=7%5E%7B%5Ccirc%7D)
[Alternate angle]
In triangle CAB:
To find AB = x foot.
Using tangent ratio:
![\tan (\theta) = \frac{Opposite side}{Adjacent Base}](https://tex.z-dn.net/?f=%5Ctan%20%28%5Ctheta%29%20%3D%20%5Cfrac%7BOpposite%20side%7D%7BAdjacent%20Base%7D)
![\tan (\angle CAB) = \frac{BC}{AB}](https://tex.z-dn.net/?f=%5Ctan%20%28%5Cangle%20CAB%29%20%3D%20%5Cfrac%7BBC%7D%7BAB%7D)
Here, BC = 50 foot and ![\angle CAB =7^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20CAB%20%3D7%5E%7B%5Ccirc%7D)
then;
![\tan (7^{\circ}) = \frac{50}{x}](https://tex.z-dn.net/?f=%5Ctan%20%287%5E%7B%5Ccirc%7D%29%20%3D%20%5Cfrac%7B50%7D%7Bx%7D)
or
![x = \frac{50}{\tan 7^{\circ}}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B50%7D%7B%5Ctan%207%5E%7B%5Ccirc%7D%7D)
![x = \frac{50}{0.1227845609}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B50%7D%7B0.1227845609%7D)
Simplify:
AB = x = 407.217321 foot
Therefore, the boat from the base of the light house is, 407.22'
96/43 = 196/43
the equation is false.
Hope this helps!
The minute hand is like an eight inch radius of a circle, whose circumference would equal 2 * PI * 8 = 50.265 inches. By moving to 8 o'clock, it travels 2/3 of the circumference or 50.265 * 2/3 = 33.510 inches
Point D is the midpoint of the outer circle that we aim to find the area of
The circle has a diameter of WZ and radii of WC and CZ
We know that YZ=YD=10 cm
Let DC be
![x](https://tex.z-dn.net/?f=x)
and CY be
![10-x](https://tex.z-dn.net/?f=10-x)
The radius of the outer circle can be written as
![8+8+x](https://tex.z-dn.net/?f=8%2B8%2Bx)
or
![10+10-x](https://tex.z-dn.net/?f=10%2B10-x)
which we can equate to find the value of
![x](https://tex.z-dn.net/?f=x)
![8+8+x=10+10-x](https://tex.z-dn.net/?f=8%2B8%2Bx%3D10%2B10-x)
![16+x=20-x](https://tex.z-dn.net/?f=16%2Bx%3D20-x)
![2x=4](https://tex.z-dn.net/?f=2x%3D4)
![x=2](https://tex.z-dn.net/?f=x%3D2)
Therefore, the radius of the circle is
![8+8+2=18](https://tex.z-dn.net/?f=8%2B8%2B2%3D18)
And hence the area of the circle is
![\pi (18^{2})](https://tex.z-dn.net/?f=%20%20%5Cpi%20%2818%5E%7B2%7D%29)
=324
Answer:
$18.43
Step-by-step explanation:
19.61 decrease 6% =
19.61 × (1 - 6%) = 19.61 × (1 - 0.06) = 18.4334