3. Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 36 inches long. What is the side length of each piece?
A. 13 inches
B. 13 √2 inches
C. 13 √3 inches
D. 26 √2 inches***
4. Find the missing value to the nearest hundredth. sin ______ = 9/16
A. 25.94 degrees
B. 29.36 degrees
C. 34.23 degrees
D. 55.77 degrees
5. Find the missing value to the nearest hundredth. cos_______ = 9/20
A. 26.74 degrees
B. 80.63 degrees
C. 63.36 degrees
D. 24.23 degrees
6. Viola drives 200 meters up a hill that makes an angle of 9 degrees with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered?
A. 1,262.8 meters
B. 200.4 meters
C. 197.5 meters
D. 31.3 meters
7. The students in Mr. Collin's class used a surveyor's measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance.
(There is a large rectangle with a triangle to its right. The bottom right of the triangle says 72 degrees and the bottom of the triangle says 100 ft.)
To the nearest foot, what is the height of the building?
A. 2,400 ft
B. 72 ft
C. 308 ft
D. 33 ft
well, #1 is wrong, since no choice works. I suspect a typo.
Yeah it was 26 sorry
in that case, 26/√2 = 13√2
the rest are just straightforward basic trig functions.
3. To find the side length of each piece of the quilt, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, we have a right triangle with one side of length 36 inches (the hypotenuse) and the other two sides equal in length (the side lengths of the quilt pieces we want to find).
Let's call the side length we're looking for "x". Applying the Pythagorean theorem, we have:
x^2 + x^2 = 36^2
Simplifying the equation:
2x^2 = 36^2
Dividing both sides by 2:
x^2 = (36^2) / 2
Taking the square root of both sides:
x = sqrt((36^2) / 2)
x = sqrt(1296 / 2)
x = sqrt(648)
x ≈ 25.4558
Therefore, the side length of each quilt piece is approximately 25.5 inches. However, among the answer choices provided, none of them match this value exactly. So, we can't determine the exact side length based on the given answer choices.
4. To find the missing value for sine, we can use the inverse sine function or arcsine function, denoted as sin^(-1) or asin. This function allows us to find the angle whose sine is equal to a given value.
In this case, we are given sin θ = 9/16. To find the angle θ, we can use the inverse sine function:
θ = sin^(-1)(9/16)
Using a calculator or a table of trigonometric values, we find:
θ ≈ 34.23 degrees
Therefore, the missing value to the nearest hundredth is 34.23 degrees, which corresponds to option C.
5. Similar to the previous question, to find the missing value for cosine, we can use the inverse cosine function or arccos function, denoted as cos^(-1) or acos. This function allows us to find the angle whose cosine is equal to a given value.
In this case, we are given cos θ = 9/20. To find the angle θ, we can use the inverse cosine function:
θ = cos^(-1)(9/20)
Using a calculator or a table of trigonometric values, we find:
θ ≈ 63.36 degrees
Therefore, the missing value to the nearest hundredth is 63.36 degrees, which corresponds to option C.
6. To find the horizontal distance Viola has covered, we can use the trigonometric relationship between the horizontal distance, the distance uphill, and the angle of inclination.
The angle of inclination is given as 9 degrees, and the distance uphill is given as 200 meters. We want to find the horizontal distance (adjacent side to the angle).
Using the trigonometric function cosine, which relates the adjacent side to the hypotenuse, we can write:
cos 9 = adjacent / 200
To find the adjacent side, we multiply both sides by 200:
adjacent = 200 * cos 9
Using a calculator or a table of trigonometric values, we find:
adjacent ≈ 197.43
Therefore, to the nearest tenth of a meter, the horizontal distance Viola has covered is approximately 197.4 meters, which corresponds to option C.
7. To find the height of the building, we can use the trigonometric relationship between the height, the distance, and the angle of elevation.
In this case, the angle of elevation (angle from their location to the top of the building) is given as 72 degrees, and the distance from the bottom of the building is given as 100 ft. We want to find the height (opposite side to the angle).
Using the trigonometric function tangent, which relates the opposite side to the adjacent side, we can write:
tan 72 = height / 100
To find the height, we multiply both sides by 100:
height = 100 * tan 72
Using a calculator or a table of trigonometric values, we find:
height ≈ 308.33
Therefore, to the nearest foot, the height of the building is approximately 308 ft, which corresponds to option C.