### All PSAT Math Resources

## Example Questions

### Example Question #51 : Right Triangles

**Possible Answers:**

**Correct answer:**

### Example Question #102 : Geometry

Kathy and Jill are travelling from their home to the same destination. Kathy travels due east and then after travelling 6 miles turns and travels 8 miles due north. Jill travels directly from her home to the destination. How miles does Jill travel?

**Possible Answers:**

**Correct answer:**

Kathy's path traces the outline of a right triangle with legs of 6 and 8. By using the Pythagorean Theorem

miles

### Example Question #103 : Geometry

**Possible Answers:**

**Correct answer:**

### Example Question #11 : Apply The Pythagorean Theorem To Find The Distance Between Two Points In A Coordinate System: Ccss.Math.Content.8.G.B.8

In order to get to work, Jeff leaves home and drives 4 miles due north, then 3 miles due east, followed by 6 miles due north and, finally, 7 miles due east. What is the straight line distance from Jeff’s work to his home?

**Possible Answers:**

2√5

10√2

6√2

15

11

**Correct answer:**

10√2

Jeff drives a total of 10 miles north and 10 miles east. Using the Pythagorean theorem (a^{2}+b^{2}=c^{2}), the direct route from Jeff’s home to his work can be calculated. 10^{2}+10^{2}=c^{2}. 200=c^{2}. √200=c. √100√2=c. 10√2=c

### Example Question #141 : Geometry

Jim leaves his home and walks 10 minutes due west and 5 minutes due south. If Jim could walk a straight line from his current position back to his house, how far, in minutes, is Jim from home?

**Possible Answers:**

√10

6√6

√5

5√5

**Correct answer:**

5√5

By using Pythagorean Theorem, we can solve for the distance “as the crow flies” from Jim to his home:

10^{2} + 5^{2} = *x*^{2}

100 + 25 = *x*^{2}

√125 = x, but we still need to factor the square root

√125 = √25*5, and since the √25 = 5, we can move that outside of the radical, so

5√5= *x*

### Example Question #111 : Plane Geometry

A square enclosure has a total area of 3,600 square feet. What is the length, in feet, of a diagonal across the field rounded to the nearest whole number?

**Possible Answers:**

85

60

95

75

100

**Correct answer:**

85

In order to find the length of the diagonal accross a square, we must first find the lengths of the individual sides.

The area of a square is found by multiply the lengths of 2 sides of a square by itself.

So, the square root of 3,600 comes out to 60 ft.

The diagonal of a square can be found by treating it like a right triangle, and so, we can use the pythagorean theorem for a right triangle.

60^{2} + 60^{2} = C^{2}

the square root of 7,200 is 84.8, which can be rounded to 85

### Example Question #51 : Right Triangles

If the length of CB is 6 and the angle C measures 45º, what is the length of AC in the given right triangle?

**Possible Answers:**

12√2

6

72

6√2

9

**Correct answer:**

6√2

Pythagorean Theorum

AB^{2} + BC^{2} = AC^{2}

If C is 45º then A is 45º, therefore AB = BC

AB^{2} + BC^{2} = AC^{2}

6^{2} + 6^{2} = AC^{2}

2*6^{2} = AC^{2}

AC = √(2*6^{2}) = 6√2

### Example Question #112 : Plane Geometry

You leave on a road trip driving due North from Savannah, Georgia, at 8am. You drive for 5 hours at 60mph and then head due East for 2 hours at 50mph. After those 7 hours, how far are you Northeast from Savannah as the crow flies (in miles)?

**Possible Answers:**

**Correct answer:**

Distance = hours * mph

North Distance = 5 hours * 60 mph = 300 miles

East Distance = 2 hours * 50 mph = 100 miles

Use Pythagorean Theorem to determine Northeast Distance

300^{2 + }100^{2 }=NE^{2 }

90000 + 10000 = 100000 = NE^{2}

NE = √100000

### Example Question #32 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A square garden has an area of 49 ft^{2}. To the nearest foot, what is the diagonal distance across the garden?

**Possible Answers:**

10

7

11

9

8

**Correct answer:**

10

Since the garden is square, the two sides are equal to the square root of the area, making each side 7 feet. Then, using the Pythagorean Theorem, set up the equation 7^{2 }+ 7^{2 }= the length of the diagonal squared. The length of the diagonal is the square root of 98, which is closest to 10.

### Example Question #113 : Plane Geometry

A man at the top of a lighthouse is watching birds through a telescope. He spots a pelican 5 miles due north of the lighthouse. The pelican flies due west for 12 miles before resting on a buoy. What is the distance, in miles, from the pelican's current resting spot to the lighthouse?

**Possible Answers:**

**Correct answer:**

We look at the 3 points of interest: the lighthouse, where the pelican started, and where the pelican ended. We can see that if we connect these 3 points with lines, they form a right triangle. (From due north, flying exactly west creates a 90 degree angle.) The three sides of the triangle are 5 miles, 13 miles and an unknown distance. Using the Pythagorean Theorem we get: