Use the Pythagorean Theorem to find the missing distances. Then, use a table of numbers whose squares are close to the value you want to approximate. Mark both values on a number line to compare them.
Plane B, see solution.
Practice makes perfect
We want to find out which plane is closer to the base of the airport tower. To do so, we will use the Pythagorean Theorem and approximate the values we will find. First, let's take a look at the given picture.
Now, we will highlight the distances between the two planes and the base of the airport tower and label them as x and y.
Notice that the distances between the planes and the base of the airport tower create two right angles. We will use this fact to find the value of x and y. To do so, let's recall the Pythagorean Theorem.
a^2+ b^2= c^2
In this formula, a and b are the lengths of the legs, and c is the length of the hypotenuse of a right triangle. Keeping this in mind, let's focus on our exercise, beginning with Plane A. We will substitute 5 for a, 6 for b, and solve the equation for x. Let's do it!
Plane A is sqrt(61) kilometers from the base of the airport tower. Now, we will approximate this square root. To do so, we will use a table of numbers whose squares are close to 61. Let's take a look.
Number
Square of Number
7
49
8
64
9
81
From the table, we can see that 61 is between 7^2 and 8^2. Because 61 is closer to 64 than to 49, we can say that sqrt(61) is a little less than 8. Let's place this number on a number line.
Now, we will focus on Plane B, beginning with the distance from the base of the airport tower. This time, we will add 5 and 2 to a distance of 7 from the base to the Plane B. That is the value of a. Then we can substitute 3 for b — the height of Plane B from the ground — into the formula
Next, we will approximate the value of sqrt(58) just like we did for the previous square root. Let's take a look at a new table.
Number
Square of Number
7
49
7.5
56.25
8
64
From the table, we can see that 58 is between 7.5^2 and 8^2. Because 58 is closer to 56.25 than to 64, we can say that sqrt(58) is little more than 7.5. We will mark this value on a number line.
From the graph, we can see that sqrt(61) is to the right of sqrt(58) on a number line. That means, we can say Plane B is closer to the base of the airport tower than Plane A.
