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Pachacha [2.7K]
2 years ago
6

You and another person are sunbathing on the beach near a lifeguard station. The other person chooses a spot that is the same di

stance from the shoreline but 11 feet closer to the station than you. The angles of elevation from you and the other person to the top of the lifeguard station are 36 degrees and 46 degrees, respectively. Estimate the height of the lifeguard station to the nearest tenth of a foot.

Mathematics
1 answer:
Schach [20]2 years ago
7 0

Answer: 26.8 feet

Step-by-step explanation:

In the figure attached you can see two right triangles  triangle ABD and a triangle ACD.

You are located at point B and the other person at point C.

The approximate height of the lifeguard station is <em>x</em>.

Keep on mind that:

tan\alpha=\frac{opposite}{adjacent}

Therefore:

<em>For the triangle ABD</em>:

tan(36\°)=\frac{x}{DC+11}    [EQUATION 1]

<em>For the triangle ACD:</em>

tan(46\°)=\frac{x}{DC}    [EQUATION 2]

Solve from DC from [EQUATION 2]:

DC=\frac{x}{tan(46\°)}

Substitute into [EQUATION 1] and solve for x:

tan(36\°)=\frac{x}{(\frac{x}{tan(46\°)}+11)}\\tan(36\°)(\frac{x}{tan(46\°)}+11)=x\\11*tan(36\°)=x-\frac{xtan(36\°)}{tan(46\°)}\\7.991=0.298x

x=26.81ft≈26.8ft

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Answer:

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15 points! I will give Brainliest and heart! Answer ASAP but with DETAIL, I need step - by - step, clear words, correct grammar.
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Hey there! I'm happy to help!

PART A

Let's look at our two equations.

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We will solve this with substitution because we have two different values for y, so it will be be very easy to substitute.

We know that y is equal to 6x-8. This means that we can replace the y in the first equation with 6x-8 and then solve for x.

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PART B

When graphing the two equations in a systems of equation, the point where they intersect is the solution. We already have our solution, so now we will just write it as a point, which is (1,-2).

Have a wonderful day! :D

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<u>Step-by-step explanation:</u>

use the product formula (ab' + a'b) to find the derivative:

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10+x-15-3x

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