3.
A ladder is leaning against a house. The distance between the base of the ladder to the house is 3 feet. The length of the ladder is 10 feet. In feet, how far above the ground does the ladder touch the house? (1 point)
4.2
9.5
10.4
14.1
4.
A wire is stretched from the top of a 26-foot pole to a point on the ground that is 15 feet from the bottom of the pole. Approximately how long is the wire in feet? (1 point)
16
21
30
37
3. 9.5
4. 21
Are they correct? Thanks
Your first answer is right. Your second answer is wrong.
is the answer 30
Yes. It's 30
Yes, your answers are correct!
To explain how to arrive at these answers:
For question 3, you have a right triangle formed by the ladder, the ground, and the side of the house. The ladder is the hypotenuse of the triangle, and the distance between the base of the ladder and the house is one of the legs. The length of the ladder is given as 10 feet. To find how far above the ground the ladder touches the house, you can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, using the theorem: (3 feet)^2 + (x feet)^2 = (10 feet)^2
Simplifying: 9 + x^2 = 100
Solving for x: x^2 = 100 - 9
x^2 = 91
x = √91
Rounding to the nearest tenth, x = 9.5 feet.
For question 4, you have a similar right triangle formed by the pole, the wire, and the distance from the bottom of the pole to the point on the ground. The height of the pole is given as 26 feet and the distance from the bottom of the pole to the point on the ground is given as 15 feet. To calculate the length of the wire, you can once again use the Pythagorean theorem.
Thus, using the theorem: (15 feet)^2 + (x feet)^2 = (26 feet)^2
Simplifying: 225 + x^2 = 676
Solving for x: x^2 = 676 - 225
x^2 = 451
x = √451
Rounding to the nearest whole number, x ≈ 21 feet.
So, your answers of 9.5 feet for question 3 and 21 feet for question 4 are correct.