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Dahasolnce [82]
2 years ago
10

Set up a right triangle model for this problem and solve by using the reference table trigonometric ratio that applies. Follow t

he models above.
A photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41°. How tall is the lighthouse?
A.45.3 yards
B.52.2 yards
C.39.4 yards
Mathematics
2 answers:
RSB [31]2 years ago
5 0
In reference to the angle of elevation (41 degrees), the adjacent side is 60 and the opposite side is the unknown.
Using tangent ratio:
tan 41 = opp/60
60 tan41 = opp
opp side = 52.2yards
LETTER B
g100num [7]2 years ago
5 0

Answer: B. 52.2 yards

Lighthouse is 52.2 yards tall.

Step-by-step explanation:

Let AB denotes the height of the lighthouse & BC denotes the distance between the base of a lighthouse and Photographer.

In Figure,  ∠ACB = 41° & ∠ABC = 90°, Threrefore,  Base is BC and perpendicular is AB.

As we know, tan(∠ACB) = \frac{Perpendicular}{Base}

∴  tan 41° = \frac{AB}{BC}

tan 41° = \frac{AB}{60}

0.869286737 = \frac{AB}{60}

AB = 52.2 yards ( approx.)

Thus, Height of the lighthouse is 52.2 yards


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The areas of two similar triangles are 72dm2 and 50dm2. The sum of their perimeters is 226dm. What is the perimeter of each of t
astraxan [27]

Answer:

Hence, the perimeter of the triangles are:

P=123.2727 dm

P'=102.7272 dm

Step-by-step explanation:

In two similar triangles:

The ratio of the areas of two triangle is equal to the square of their perimeters.

Let A and A' represents the area of two triangles and P and P' represents their perimeter.

Then they are related as:

\dfrac{A}{A'}=\dfrac{P^2}{P'^2}

We are given:

A=72 dm^2  , A'=50 dm^2

and P+P'=226 dm.-----------(1)

i.e. \dfrac{72}{50}=\dfrac{P^2}{P'^2}\\\\\dfrac{36}{25}=\dfrac{P^2}{P'^2}

on taking square root on both the side we get:

\dfrac{P}{P'}=\dfrac{6}{5}\\\\P=\dfrac{6}{5}P'

Now putting the value of P in equation (1) we obtain:

\dfrac{6}{5}P'+P'=226\\\\\dfrac{6P'+5\times P'}{5}=226\\\\\dfrac{6P'+5P'}{5}=226\\\\11P'=226\times 5\\\\11P'=1130\\\\P'=\dfrac{1130}{11}=102.7272

Hence,

P=226-102.7272=123.2727

Hence, the perimeter of the triangles are:

P=123.2727 dm

P'=102.7272 dm

6 0
3 years ago
URGENT ANSWER FAST PLEASE
xeze [42]
410.3ft^3. is correct





volume of the sphere with 3ft radius :
\frac{4  \times  \pi \times 3 \times 3 \times 3}{3}  = 113




volume of the sphere with 5ft radius:
\frac{4 \times \pi \times 5 \times 5 \times 5}{3}  = \frac{1570}{3}   = 523.3



difference
523.3 - 113 = 410.3





good luck
7 0
3 years ago
Estimate the following sum by clustering.
Kryger [21]
The answer would be 60. By rounding, 14.2=14; 15.51=16; 14.99=15; 15.8=16.
14+15+16+16=61
Rounding: 61=60
4 0
2 years ago
Read 2 more answers
Need help please!!!<br>Given parallelogram MNOP if PN=27 what is NQ ​
likoan [24]

9514 1404 393

Answer:

  NQ = 13.5

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. NQ is half of NP, so is ...

  NQ = PN/2 = 27/2

  NQ = 13.5

8 0
2 years ago
What does the "mean" applies to math mean?
Elodia [21]
It is the same thing as the average you add everything up then you divide by the number of numbers you added together 
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3 years ago
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