4. A carpenter wants to be sure that the corner of a building is square and measures 6.0 ft and 8.0 ft along
the sides. How long should the diagonal be?
A. 12 ft
B. 10 ft
C. 11 ft
D. 14 ft
5. A wheel 5.00 ft in diameter rolls up a 15.0° incline. How far above the base of the incline is the top of
the wheel after the wheel has completed one revolution?
A. 4.07 ft
B. 13.1 ft
C. 8.13 ft
D. 9.07 ft
7. A surveyor must divert her path from point C by proceeding due south for 300 ft to point A. The
surveyor determines that point B, which is due east of point C, is N49°E from point A. What is the distance
from point C to point B?
A. 350 ft
B. 375 ft
C. 360 ft
D. 370 ft
8. Which of the following pairs of angles are coterminal?
A. 25° and –25°
B. 100° and 620°
C. 30° and 60°
D. 390° and 750°
9. A 6.00-foot person is casting a shadow of 4.20 feet. What time of the morning is it if the sun rose at
6:15 AM and will be directly overhead at 12:15 PM?
A. 8:35 AM
B. 9:40 AM
C. 8:58 AM
D. 9:55 AM
10. Find the numerical measure of the largest angle of a triangle whose angle measures are 6x – 10°, 3x +
30°, and 2(45° – x).
A. 60°
B. 70°
C. 50°
D. 10°
11. A stairway must be built to a deck that is 20 feet above ground level. To the nearest half foot, how far
from the base of the deck, on ground level, should the beginning of the stairway be placed so that the
stairway forms a 60° angle from the ground?
A. 12 ft
B. 11 ft
C. 35 ft
D. 11.5 ft
13. If a tree casts a shadow of 12 feet at the same time that a 6-foot person casts a shadow of 2½ feet,
what is the length of the tree to the nearest foot?
A. 24 ft
B. 5 ft
C. 29 ft
D. 22 ft
16. How many degrees does Earth turn during an eight-hour school day? (Assume that Earth makes one
revolution every 24 hours.)
A. 120°
B. 8°
C. 3°
D. 90°
17. In a right triangle with ã the right angle, b = 86.5 and c = 125.8. What is â ?
A. 43.2°
B. 46.4°
C. 46.6°
D. 43.4°
18. Find the height of the Barrington Space Needle if the angle measured from the ground 1000 ft
(measured to the nearest foot) from the point on the ground directly below the top of the needle is 58.15°.
A. 1,610 ft
B. 621.2 ft
C. 1,895 ft
D. 527.7 ft
20. When viewing Angel Falls (the world's highest waterfall) from Observation Platform A, located on the
same level as the bottom of the waterfall, we calculate the angle of elevation to the top of the waterfall to
be 69.30°. From Observation Platform B, which is located on the same level exactly 1000 feet from the
first observation point, we calculate the angle of elevation to the top of the waterfall to be 52.90°. How
high is the waterfall?
A. 2,643 ft
B. 998.5 ft
C. 2,646 ft
D. 1,322 ft
dont homework dump
A stairway must be built to a deck that is 20 feet above ground level. To the nearest half foot, how far from the base of the deck, on ground level, should the beginning of the stairway be placed so that the stairway forms a 60° angle from the ground?
What i did to get the answer to problem 16
is to ( Multiply 8*360 = 2880/24 )which gives us 120 and that's the answer.
4. To find the length of the diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides. In this case, the two sides are 6.0 ft and 8.0 ft.
So, the length of the diagonal can be found as follows:
diagonal^2 = 6.0^2 + 8.0^2
diagonal^2 = 36 + 64
diagonal^2 = 100
Taking the square root of both sides:
diagonal = √100
diagonal = 10 ft
Therefore, the diagonal should be 10 ft.
Answer: B. 10 ft
5. When a wheel rolls up an incline, it forms a right triangle with the base of the incline. The height of the triangle represents how far above the base of the incline the top of the wheel is.
To find the height, we can use trigonometry. Specifically, we can use the sine function, which relates the opposite side (height) to the hypotenuse (diameter of the wheel) and the angle of inclination.
In this case, the diameter of the wheel is given as 5.00 ft and the angle of inclination is 15.0°.
Using the formula:
sin(angle) = opposite/hypotenuse
We can rearrange the formula to solve for the height:
opposite = sin(angle) * hypotenuse
Plugging in the values:
opposite = sin(15.0°) * 5.00 ft
Calculating the value:
opposite = 0.2588 * 5.00 ft
opposite ≈ 1.294 ft
Therefore, the top of the wheel is approximately 1.294 ft above the base of the incline.
Answer: B. 13.1 ft
7. To determine the distance from point C to point B, we can use the concept of vector addition.
First, we find the horizontal and vertical components of the vector from A to B. Since point B is due east of point C, its horizontal component is 300 ft. And since it is N49°E from point A, the vertical component can be found using trigonometry.
The vertical component is given by:
vertical component = 300 ft * sin(49°)
Plugging in the values:
vertical component = 300 ft * sin(49°)
vertical component ≈ 229.63 ft
Next, we use the horizontal and vertical components to find the magnitude of the vector from A to B using the Pythagorean theorem.
The magnitude is given by:
distance from A to B = √((horizontal component)^2 + (vertical component)^2)
Plugging in the values:
distance from A to B = √((300 ft)^2 + (229.63 ft)^2)
distance from A to B ≈ 377.11 ft
Therefore, the distance from point C to point B is approximately 377.11 ft.
Answer: B. 375 ft
(To be continued...)