105k views
1 vote
Help please I did them and got all wrong LOL..............

Help please I did them and got all wrong LOL..............-example-1
User Obto
by
8.7k points

1 Answer

6 votes

Answer:

1. Choice (2) 13

2. Choice (3) 8.1

3. Choice (3) 95 to 105 ft

4. Choice (3) 96 in

Explanation:

All the problems use the Pythagorean theorem
The Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared.


c^(2) = a^(2) + b^(2)

or


c = \sqrt{a^(2) + b^(2)}

where c is the hypotenuse and a, b the shorter sides.

This means that given any two of the three sides of a right triangle we can compute the length of the third side

For example if we were given the hypotenuse c and side b, we can solve for side a by:


a = \sqrt{c^(2) - b^(2)}

If we were given side a and asked to solve for side b then
b = \sqrt{c^{2} - a^{2}}

Frankly it does not matter which you choose as side a and side b.

Question 1
The distance from the foot of the ladder to the wall can be taken to be side a and is equal to 8ft

So b = 8ft

The length of the ladder is the hypotenuse c = 15 feet

a = \sqrt{c^(2) - b^(2)} \\\\a = \sqrt{15^(2) - 8^(2)}\\\\a = √(225 - 64)\\\\a = √(161)\\\\a = 12.68857754045 \\\\

Rounded to nearest foot, that would be 13 feet So choice (2)

Question 2

The points J and K have the following coordinates as indicated on the graph.

J(-3, 2)

K (1, -5)

The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:



d = \sqrt {(x_(2) - x_(1))^2 + (y_(2) - y_(1))^2}

For:

(X1, Y1) = (-3, 2)

(X2, Y2) = (1, -5)


d = \sqrt {(1 - (-3))^2 + (-5 - 2)^2}\\\\d = \sqrt {(4)^2 + (-7)^2}\\\\d = \sqrt {{16} + {49}}\\\\d = \sqrt {65}\\\\d = 8.062258\\\\\text{Rounded to the nearest 10th it would be \boldsymbol{8.1}}\\\\ So choice (3)

Question 3

This again involves a right triangle as shown in the figure
The sides are a = AC = 60 and b = BC = 80 and we are asked to find the length of AC which is the hypotenuse of ΔABC

Use the Pythagorean Theorem directly

c = \sqrt{a^(2) + b^(2)}}\\\\a = \sqrt{60^(2) + 80^(2)}\\\\c = √(3600 + 6400)}\\\\c = √(10000)}\\\\c = 100}\\\\

Answer 100 feet so choice (3): from 95 to 105 ft

Question 4

The brace is one of the shorter sides, with the platform top as the hypotenuse.

Let's use a for the brace, b for the 40 in side and c for the hypotenuse = 104 in

So we have to compute for b using the formula:


b = \sqrt{c^(2) - a^(2)}

Using the given values, this would be:


b = \sqrt{104^(2) - 40^(2)}\\\\b = √(10816 - 1600)\\\\b = √(9216)\\\\b = 96\\\\

which would be choice (3)

User Mike Shepard
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories