9514 1404 393
Answer:
b = 71 m
A = 83°
C = 29°
Step-by-step explanation:
Many calculators can solve triangles. Apps are available for phone and tablet, or on the internet, like the one used here. In general, it takes less time to use one of these than to type your question into Brainly.
Given two sides and the angle between them, the Law of Cosines is the appropriate relation to use for finding the third side.
b = √(a² +c² -2ac·cos(B))
b = √(76² +37² -2·76·37·cos(67.75°)) ≈ √5015.48
b ≈ 70.82005 ≈ 71 . . . meters
__
One a side and its opposite angle are known, the remaining angles are found using the Law of Sines.
sin(A)/a = sin(B)/b
A = arcsin(a·sin(B)/b) = arcsin(76·sin(67.75°)/70.82005) ≈ 83.33°
A ≈ 83°
C = arcsin(37·sin(67.75°)/70.82005) ≈ 28.92°
C ≈ 29°
Or, you can find the remaining angle from 180° -68° -83° = 29°.
The radius of the area the sprinkler has watered is 8.06 yards.
<h3>What is Rotation ?</h3>
Rotation is spinning around a fixed point with a fixed radius in circular motions.
It is given that a sprinkler rotates 360 degree
The area watered is 204 sq. yards
Radius = ?
A sprinkler rotates in circle
Therefore the area of the circle = π r²
204 = π r²
204 * 7 /22 = r²
r² = 64.91
r = 8.06 yards
Therefore the radius of the area the sprinkler has watered is 8.06 yards.
To know more about Rotation
brainly.com/question/1571997
#SPJ1
Stop with the links don’t work
81 inches converted to feet is 6.75 feet
Therefore the hour hand travels 40.192in in 5 hours
<h3>
How to calculate the area of a sector</h3>
A sector is said to be a part of a circle made of the arc of the circle along with its two radii.
The formula for calculating the area of a sector is expressed as;
A = r²β/2
where
r is the radius of the circle
β is the angle subtended
Since the the hour hand travel during 5 hours, the subtended angle by the sector will be;
β = 360/5
β = 72 degrees
Given the following parameters
r = 16/2
r = 8in
Substitute into the formula
A = 8²(72π)/360
A = 40.192in
Therefore the hour hand travels 40.192in in 5 hours
Learn more on area of a sector here: brainly.com/question/22761976
#SPJ1
