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____ [38]
3 years ago
13

looks out from the crown of the Statue of Liberty, approximately 250 ft above ground. The tourist sees a ship coming into the ha

rbor and measures the angle of depression as 18°. Find the distance from the base of the statue to the ship to the nearest foot.

Mathematics
1 answer:
Zigmanuir [339]3 years ago
3 0

Answer:

The distance from the base of the statue to the ship is 771.60 ft

Step-by-step explanation:

Refer the attached figure

Height of statue AB= 250 feet

The tourist sees a ship coming into the harbor and measures the angle of depression as 18°.

So, ∠ACB = 18°

We are supposed to find the distance from the base of the statue to the ship i.e. BC

In ΔABC

Tan \theta = \frac{Perpendicular}{Base}

Tan 18^{\circ}=\frac{AB}{BC}

Tan 18^{\circ}=\frac{250}{BC}

BC=\frac{250}{Tan 18^{\circ}}

BC=\frac{250}{0.324}

BC=771.60 ft

Hence the distance from the base of the statue to the ship is 771.60 ft

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How are the values of -4^3 and 4^-3 alike and how do they differ?
BartSMP [9]

Answer:

(-4)³ = -64

(4)⁻³ = 1/64

Step-by-step explanation:

( - 4) {}^{3}  =  ( - 4) \times ( - 4) \times ( - 4) =  - 64 \\

{4}^{ - 3}  =  (\frac{1}{4} ) {}^{3}  \\

({ \frac{1}{4} )}^{3}  =  \frac{1}{4}  \times  \frac{1}{4}  \times  \frac{1}{4}  =  \frac{1}{64}  \\

4 0
2 years ago
What is the equation of the graph below? A graph shows a parabola that opens up with a vertex at negative three comma negative o
Tomtit [17]

Answer:

y=(x+3)^2-1\\y=x^2+6x+8

Step-by-step explanation:

Given:

Vertex of the parabola is, (h,k)=(-3,-1)

Equation of the parabola in vertex form is given as:

y=(x-h)^2+k

Plug in h=-3,k=-1. This gives,

y=(x-(-3))^2+(-1)\\y=(x+3)^2-1

Therefore, the equation of the given graph is

y=(x+3)^2-1\\y=x^2+6x+8.

5 0
3 years ago
PLEASE EXPLAIN TOO SO I CAN SOLVE OTHER SIMILAR ONES.
jeka57 [31]

Answer: x = 30' , y = 45'

hope this helps

Step-by-step explanation:

U is 90' it's a right triangle

well simple VRT you already know 2 angles which is 60' and 90'

R = 60'

V = 90'

T = x

you know that a triangle = 180'

so you do

180 - 60 - 90 = x

30 = x

if you want to do y

then you already know that U is 90' on both sides.

since you also know S,

S = 45'

U = 90'

V = y

180 - 90 - 45 = y

45 = y

4 0
2 years ago
What is the area of the figure:
Luba_88 [7]

For this case we have that the area of the triangle is given by:

A = \frac {b * h} {2}

Where:

b: It's the base

h: It's the height

We have to:

cos (45) = \frac {b} {24}\\b = 24 * cos (45)\\b = \frac {\sqrt {2}} {2} * 24\\b = 12 \sqrt {2}

The atura will be given by:

sin (45) = \frac {h} {24}\\h = 24 * sin (45)\\h = \frac {\sqrt {2}} {2} * 24\\h = 12 \sqrt {2}

So, the area is:

A = \frac {12 \sqrt {2} * 12 \sqrt {2}} {2}\\A=\frac{(12\sqrt{2})^2}{2}\\A = 144

Answer:

144

6 0
3 years ago
Read 2 more answers
6x - 2y = 26<br><br> 2x + 3y = 5<br><br> Solve for X and Y
Softa [21]

Answer:

y is equal to -1

x is equal to 4

Step-by-step explanation:

The first thing you would do is multiply the bottom equation by a negative 3. You will get - 6x - 9y = -15. Keep the top equation the same. Both of the 6x's cancel. You then get -11y = 11 so y is equal to negative 1.

Since you have Y, you can now plug that in to any equation to find the value of x. -6x - 2(-1) = 26. You're left with 4. Plug both of the values into each equation to double check.

7 0
3 years ago
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