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34kurt
3 years ago
6

Set up a right triangle model for this problem and solve by using a calculator. Follow the models above,

Mathematics
1 answer:
irakobra [83]3 years ago
8 0

<em><u>Question:</u></em>

Set up a right triangle model for this problem and solve by using a calculator. Follow the 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?

<em><u>Answer:</u></em>

The height of lighthouse is 52.2 yards

<em><u>Solution:</u></em>

Given that 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 degree

The diagram is attached below

Consider a right angled triangle ABC

AB is the height of the lighthouse

BC is the distance between the base of a lighthouse and Photographer

As per given, BC = 60 yards

Angle between the  ground and the top of the lighthouse is 41 degree

Angle ACB = 41 degree

To find: height of lighthouse i.e AB = ?

We know that,

tan(\angle ACB) = \frac{Perpendicular}{Base}

Here Base is BC and perpendicular is AB

\tan 41^{\circ}=\frac{A B}{B C}

Substituting the values,

\begin{aligned}&\tan 41^{\circ}=\frac{A B}{60}\\\\&0.8692=\frac{A B}{60}\\\\&A B=0.8692 \times 60=52.157 \approx 52.2\end{aligned}

Thus the height of lighthouse is 52.2 yards

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4 0
3 years ago
John has two colored varieties of water bottles: white water bottles and black water bottles. The total number of water bottles
mixas84 [53]

Answer:

15 black water bottles

Step-by-step explanation:

let w represent white water bottles, and let b represent black water bottles.

set up a system of equations:

w+b=20

w+2b=35

(the top equation shows that the number of white water bottles he sold and the number of black water bottles he sold equals to 20, since it says that the total number of water bottles is 20. the bottom equation shows that white water bottles cost $1, and black water bottles cost $2, and that the total amount of money he got from selling them is $35).

in the top equation, isolate w:

w+b=20

w=20-b

now we do substitution. in the bottom equation, substitute 20-b for w:

w+2b=35

20-b+2b=35

then, solve:

b+20=35

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this means that he sold 15 black water bottles.

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73,404+27,865 what does it equal
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3 years ago
What is the answer to the problem 2/3x-40=5/6(x+36)
miss Akunina [59]

2/3x-40=5/6(x+36)

multiply each side by 6 to get rid of the fraction

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