Answer:
m∠ABC = 74
Step-by-step explanation:
The sum of the measures of three angles of any triangle is invariably equal to the straight angle, also expressed as 180 °
So you subtract the given measurements of ∠BAC (76°) and ∠ ACB (19°) from 180. 180-76-19 = 74
The measurement of angle ABC is 74°
Answer: The garden has dimensions 30 ft wide X 60 ft long
Step-by-step explanation:
Denote by W the width of the garden and L the length of the garden (longer side) as in the figure attached. The red sides on the figure represent the parts of the garden that require fencing.
L is also the measure of a vertical side of the garden, because a rectangle consists only of vertical and horizontal sides.
We know that the barn is parallel to the longer (vertical) side, so only one of the vertical sides L of the rectangle needs fencing. The other two parts correspond to the horizontal sides of the rectangle so they require 2W feet of fencing. Altogether, the 120 ft of fencing enclose the L+2W ft of the fence, then 120=L+2W. Because the longer side is twice the width, we have that L=2W, so 120=2W+2W=4W. From here, W=30 ft and L=2(30)= 60ft.
Answer:
r = 5
Step-by-step explanation:
To solve for r, plug in the change in x values and change in y values, since the hypotenuse is simply the diagonal of both the y-coordinate and x-coordinates shown via drawing legs on the vertical and horizontal axis. So, since (0,0) is the initial point, r = sqr[(-4-0)^2 + (-3-0)^2 = sqr(16 + 9) = 5.
Now, the angle theta is the angle in which the sine, cosine, and tangent ratios are found. Simply use opposite over hypotenuse for sine, adjacent over hypotenuse for cosine, and opposite over adjacent for tangent using theta as the angle in which these values are obtained.
Answer: 256 feet
Step-by-step explanation:
Base Surface Area = 162
= 256 feet2
Lateral Surface Area =
2×16× √
( 16 )2 + 202
2
= 689.30109531322 feet2
Total Surface Area = 945.30109531322 feet2
