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2 years ago

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A boat is anchored 2.2 km due south of a lighthouse. Along the shore, the town of Beachton is 16.8 km due east of the lighthouse

. Enter a number in the box to correctly complete the statement. Round the answer to the nearest tenth.

1 answer:

Vesnalui [34]2 years ago

7 0

First draw a right triangle using the lighthouse as reference. Draw a dot (lighthouse) draw a line downward (south) with 2.2 km measurement. Next, draw a line to the right of the lighthouse (16.8 km)

The two legs are 2.2 km and 16.8 km. To complete the statement, we need to solve for the hypotenuse of the right triangle.

Using the Pythagorean Theorem:

Assign a = 2.2 km
b = 16.8 km

so,

c^2 = a^2 + b^2

2.2^2 + 16.8^2 = c^2

Therefore, the value of c is 16.94 km.

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Answer:

The age of each person is:

Jess is <u>21</u> years old.
Mac is <u>66</u> years old.

Step-by-step explanation:

To solve this problem you must make two equations. First, we name Jess and Mac as variables:

j = Jess age.

m = Mac age.

Now we make the equations, the first equation has the information "Jess is 12 years less than half as old as Mac":

1. $j=(\frac{m}{2})-12$

The second equation has the information "The sum of their age is 87":

2. $j+m=87$

Now, we replace the first equation in the second one:

$(\frac{m}{2}-12) +m=87$

And we operate:

$\frac{m-24}{2} +m=87$
$\frac{m-24+2m}{2}=87$
$\frac{3m-24}{2}=87$

We clear the variable m:

$3m-24=87*2$
$3m=174+24$
$m=\frac{198}{2}$
$m=66$

How we know Mac's age is 66 years old, we can identify Jess' age with the second equation:

$j+m=87$

We replace the value of m:

$j+66=87$

And clear the variable j:

$j=87-66$
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In the end, Jess's age is 21 years old.

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