Use the image to answer the question.
A right triangle shows the base with a value of 3, the hypotenuse on the left with a value of 15, and the perpendicular side to the base on the right with a question mark.
Apply the Pythagorean Theorem to find the unknown side length in the given triangle. Round your answer to the nearest tenth.
(1 point)
Responses
234
234
15.3
15.3
216
216
14.7
To find the unknown side length in the right triangle, we 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.
Let's denote the unknown side length as x.
According to the theorem, we have the equation:
hypotenuse^2 = base^2 + perpendicular side^2
Substituting the given values, we have:
15^2 = 3^2 + x^2
Simplifying, we get:
225 = 9 + x^2
Subtracting 9 from both sides, we have:
216 = x^2
Taking the square root of both sides, we get:
x = √216
Rounding this to the nearest tenth, we get:
x ≈ 14.7
Therefore, the unknown side length is approximately 14.7.
If a right triangle has legs that are both 12 cm long, how long is the hypotenuse? Round the answer to the nearest hundredth.(1 point)
Responses
17.0
17.0
288
288
16.97
16.97
Not enough information is given to solve the problem.
We can use the Pythagorean Theorem to find the length of the hypotenuse in a right triangle.
Let's denote the length of the hypotenuse as c.
According to the theorem, we have the equation:
c^2 = leg1^2 + leg2^2
Substituting the given values, we have:
c^2 = 12^2 + 12^2
Simplifying, we get:
c^2 = 144 + 144
c^2 = 288
Taking the square root of both sides, we get:
c = √288
Rounding this to the nearest hundredth, we get:
c ≈ 16.97
Therefore, the length of the hypotenuse is approximately 16.97 cm.
Sylvia is replacing a piece of siding on her house. To make the 12 ft. ladder stable, the bottom of the ladder needs to be 6 ft. from the base of her house. Applying the Pythagorean Theorem and rounding to the nearest tenth, how high will the ladder reach so that Sylvia can replace the siding?(1 point)
Responses
108 ft.
108 ft.
13.4 ft.
13.4 ft.
10.4 ft.
10.4 ft.
180 ft.
An electric pole has a support cable that is attached to the pole 20 ft. from the ground. The cable is anchored on the ground 10 ft. from the base of the pole. How long is the cable? Round to the nearest tenth.(1 point)
Responses
300 ft.
300 ft.
17.3 ft.
17.3 ft.
500 ft.
500 ft.
22.4 ft.
To find the length of the cable, we can apply the Pythagorean Theorem.
Let's denote the length of the cable as c.
According to the theorem, we have the equation:
c^2 = height of pole^2 + distance from pole base to anchor point^2
Substituting the given values, we have:
c^2 = 20^2 + 10^2
Simplifying, we get:
c^2 = 400 + 100
c^2 = 500
Taking the square root of both sides, we get:
c = √500
Rounding this to the nearest tenth, we get:
c ≈ 22.4
Therefore, the length of the cable is approximately 22.4 ft.
A streetlight post needs some extra support for potential bad weather and high winds. The city wants to install metal support brackets on the light post. Each bracket will be braced into the ground and will then attach to a point on the pole that is 4.5 ft. from the ground. Each bracket is 6.5 ft. long. How far from the base of the pole should each bracket be braced in the ground? Round to the nearest tenth.(1 point)
Responses
4.7 ft.
4.7 ft.
62.5 ft.
62.5 ft.
22.0 ft.
22.0 ft.
7.9 ft.
To determine the height the ladder will reach, we can apply the Pythagorean Theorem.
Let's denote the height of the ladder as h.
According to the theorem, we have the equation:
h^2 = ladder base^2 + ladder height^2
Substituting the given values, we have:
h^2 = 6^2 + 12^2
Simplifying, we get:
h^2 = 36 + 144
h^2 = 180
Taking the square root of both sides, we get:
h = √180
Rounding this to the nearest tenth, we get:
h ≈ 13.4
Therefore, the height the ladder will reach is approximately 13.4 ft.
To determine how far from the base of the pole each bracket should be braced in the ground, we can apply the Pythagorean theorem.
Let's denote the distance from the base of the pole to the brace point as x.
According to the theorem, we have the equation:
x^2 = height of pole^2 + length of bracket^2
Substituting the given values, we have:
x^2 = 4.5^2 + 6.5^2
Simplifying, we get:
x^2 = 20.25 + 42.25
x^2 = 62.5
Taking the square root of both sides, we get:
x = √62.5
Rounding this to the nearest tenth, we get:
x ≈ 7.9
Therefore, each bracket should be braced in the ground approximately 7.9 ft from the base of the pole.