Use what you know about the relationships in 30-60-90 right triangles to solve the following problem. A stained-glass window is in the shape of an equilateral triangle with sides that are 36 inches long. How long is the perpendicular bisector of any side?(1 point)
Responses
9 inches
9 inches
183–√ inches
18 Start Root 3 End Root inches
36 inches
36 inches
18 inches
The perpendicular bisector of any side in an equilateral triangle divides the side into two equal segments. Since the sides of the equilateral triangle are 36 inches long, the perpendicular bisector of any side would be half of that length, which is 18 inches.
If the side opposite a 60-degree angle in a 30-60-90 right triangle is 73–√ cm long, how long is the hypotenuse?(1 point)
Responses
28 cm
28 cm
7 cm
7 cm
14 cm
14 cm
73–√ cm
In a 30-60-90 right triangle, the ratio of the side opposite the 30-degree angle to the hypotenuse is 1:2.
So, if the side opposite the 60-degree angle is 73–√ cm long, then the hypotenuse would be twice that length, which is 2(73–√) cm or 146–2√ cm.
If the side opposite a 60-degree angle in a 30-60-90 right triangle is 73–√ cm long, how long is the hypotenuse?(1 point)
Responses
28 cm
28 cm
7 cm
7 cm
14 cm
14 cm
7√3 cm
In a 30-60-90 right triangle, the ratio of the side opposite the 30-degree angle to the hypotenuse is 1:2.
So, if the side opposite the 60-degree angle is 73–√ cm long, then the hypotenuse would be twice that length, which is 2(73–√) cm or 146–2√ cm. However, this is not one of the given options.
Another way to find the length of the hypotenuse is by using the 30-60-90 triangle relationship: the hypotenuse is twice the length of the side opposite the 30-degree angle.
Since the side opposite the 60-degree angle is 73–√ cm long, the hypotenuse would be 2 times that length, which is 2(73–√) cm or 146–2√ cm.
Therefore, none of the given options accurately represent the length of the hypotenuse.
What is the length of the hypotenuse of a 30-60-90 triangle if the side opposite the 60-degree angle is 63–√ ?(1 point)
Responses
12√3
6
2√3
12
In a 30-60-90 right triangle, the ratio of the side opposite the 30-degree angle to the hypotenuse is 1:2√3.
If the side opposite the 60-degree angle is 63–√, then the hypotenuse would be (2√3)(63–√) or 126–2.
Therefore, the correct response is 126–2.
Jamila keeps alpacas on a 1-acre, square lot near her home.
She has 6 alpacas and wants to build a fence diagonally to split the herd in two.
If an acre is 209 feet long, how many feet, to the nearest foot, of fencing does Jamila need?
(1 point)
Responses
148 feet
148 feet
362 feet
362 feet
296 feet
296 feet
247 feet
To find the length of the diagonal of the square lot, we can use the Pythagorean theorem.
Since the lot is a square with an area of 1 acre, each side of the square would be √1 acre = 1 acre = √(209^2) square feet = 209 feet.
Now, we can use the Pythagorean theorem to find the length of the diagonal (d).
d^2 = (side length)^2 + (side length)^2
d^2 = 209^2 + 209^2
d^2 = 2(209^2)
d = √(2(209^2))
d ≈ 295.765 feet.
Rounding to the nearest foot, Jamila would need approximately 296 feet of fencing.
Therefore, the correct response is 296 feet.