Question 9.3E2: Crossing a Moat The moat surrounding a castle is 18 ft wide ......

A Survey of Mathematics with Applications [1175320]

Crossing a Moat

The moat surrounding a castle is 18 ft wide and the wall by the moat of the castle is 24 ft high (see Fig. 9.32). If an invading army wishes to use a ladder to cross the moat and reach the top of the wall, how long must the ladder be?

f9.32

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

The moat, the castle wall, and the ladder form a right triangle. The moat and the castle wall form the legs of the triangle (sides a and b), and the ladder forms the hypotenuse (side c). By the Pythagorean theorem,

c^2  =  a^2  +  b^2 \\ c^2  =  (18)^2  +  (24)^2 \\ c^2  =  324  +  576 \\ c^2  =  900 \\ \sqrt{c^2}  =  \sqrt{900} \ \text{Take the square root of both sides of the equation.} \\ c = 30

Therefore, the ladder would need to be at least 30 ft long.

Related Answered Questions

Question: 9.3.6

A Commutative Group Construct a mod 5 addition table and show that the mathematical system is a commutative group. Assume that the associative property holds for the given operation. ...

Verified Answer:

The set of elements in modulo 5 arithmetic is {0, ...

Question: 9.5E6

A Glide Reflection of a Parallelogram Construct a glide reflection of parallelogram ABCD, shown in Fig. 9.70, using translation vector v and reflection line l. ...

Verified Answer:

To construct the glide reflection of parallelogram...

Question: 9.2E2

Similar Figures Consider the similar figures in Fig. 9.21. Determine a) the length of side BC. b) the length of side PQ. ...

Verified Answer:

a) We will represent the length of side

\o...

Question: 9.2E1

Angles of a Hexagon The surfaces of the heads of many bolts are in the shape of regular hexagons. A regular hexagon is a six-sided figure with all the sides the same length and all interior angles with the same measure. See Fig. 9.19. Determine a) the measure of an interior angle. b) the measure of ...

Verified Answer:

a) Using the formula (n - 2)180°, we can determin...

Question: 9.2E3

Using Similar Triangles to Find the Height of a Tree Monique Currie plans to remove a tree from her backyard. She needs to know the height of the tree. Monique is 6 ft tall and determines that when her shadow is 9 ft long, the shadow of the tree is 45 ft long (see Fig. 9.22 on page 494). How tall ...

Verified Answer:

We will let x represent the height of the tree. Fr...

Question: 9.2E4

Congruent Triangles Triangles ABC and A′B′C′ in Fig. 9.23 are congruent. Determine a) the length of side A′C′. b) the length of side AB. c) m∡C′A′B′. d) m∡ACB. e) m∡ABC. ...

Verified Answer:

Because ΔABC is congruent to ΔA′B′C′, we know that...

Question: 9.2E5

Angles of a Trapezoid Trapezoid ABCD is shown in Fig. 9.24. a) Determine the measure of the interior angle, x. b) Determine the measure of the exterior angle, y. ...

Verified Answer:

a) We know that each of the two right angles in t...

Question: 9.3E1

Sodding a Lacrosse Field Rob Marshall wishes to replace the grass (sod) on a lacrosse field. One pallet of Bethel Farms sod costs $175 and covers 450 square feet. If the area to be covered is a rectangle with a length of 330 feet and a width of 270 feet, determine a) the area to be covered with sod ...

Verified Answer:

a) The area to be covered is

A = l ⋅ w...

Question: 9.3E3

Comparing Pizzas Victoria Montoya wishes to order a large cheese pizza. She can choose among three pizza parlors in town: Antonio’s, Steve’s, and Dorsey’s. Antonio’s large cheese pizza is a round 16-in.-diameter pizza that sells for $15. Steve’s large cheese pizza is a round 14-in.-diameter pizza ...

Verified Answer:

To determine the best value, we will calculate the...

Question: 9.3E4

Determining the Shaded Area Determine the shaded area. Use the π key on your calculator and round your answer to the nearest hundredth. ...

Verified Answer:

To determine the area of the shaded region, we wil...