Answer:
Two possible lengths for the legs A and B are:
B = 1cm
A = 14.97cm
Or:
B = 9cm
A = 12cm
Step-by-step explanation:
For a triangle rectangle, Pythagorean's theorem says that the sum of the squares of the cathetus is equal to the hypotenuse squared.
Then if the two legs of the triangle are A and B, and the hypotenuse is H, we have:
A^2 + B^2 = H^2
If we know that H = 15cm, then:
A^2 + B^2 = (15cm)^2
Now, let's isolate one of the legs:
A = √( (15cm)^2 - B^2)
Now we can just input different values of B there, and then solve the value for the other leg.
Then if we have:
B = 1cm
A = √( (15cm)^2 - (1cm)^2) = 14.97
Then we could have:
B = 1cm
A = 14.97cm
Now let's try with another value of B:
if B = 9cm, then:
A = √( (15cm)^2 - (9cm)^2) = 12 cm
Then we could have:
B = 9cm
A = 12cm
So we just found two possible lengths for the two legs of the triangle.
Answer:
- a) Plots are similar
- b) x= 5577 feet
Step-by-step explanation:
<em>Refer to attached</em>
<h3>Question</h3>
- a) Are the plots of land similar?
- b) Find to the exact value of x and rounded to the nearest tenth?
<h3>Solution</h3>
The small triangle have missing angle of 180° - (52° + 58°) = 70°
This is indicating both triangles have same 3 angle measures.
Since all angles are same, the triangles are similar.
<u>Corresponding sides, against corresponding angles are:</u>
<u>As per property of similarity, the ratio of corresponding sides is same</u>
- 6180/8240 = x/7436
- x = 6180*7436/8240
- x = 5577 feet
Remark
You cannot give an answer to this unless you are give the fastest speed of a swimmer. That stat is not an easy one to decide upon. At what distance for example or do you eliminate distance? Since this is a college level question, I don't think it unreasonable that you have to research raw distance over fastest time.
The fastest speed I can find is 100 meters in 46.91 seconds. That means that the actual speed of the swimmer is 100 meters / 46.91 = 2.132 meters / second.
Givens
Set up a proportion with the numbers found and given
Speed of ball / speed of swimmer = 21.12 / 1
Speed of ball = x
Solution
Speed of swimmer = 2.132 m/s
x / 2.132 = 21.12 / 1 Multiply Both sides by 2.132
x = 21.12 * 2.132 / 1
x = 45.02 m/s
Answer
45.02 m/s
Let's calculate the actual area: it is 11*5.6*7.2 or 443.52 cubic meters. Is the 100+ cubic meters error reasonable? :)
Formula: V = (2/3) π r 3.
Radius is 3cm.
So, now we can plug it in to solve for the volume.
V = (2/3) π 3^3
First, let's multiply 3^3.
3^3 = 27
Then, 27 x π = 84.82
After, multiply by 2/3.
84.82 x 2/3 = 56.55
Lastly, round 56.55 to the nearest tenth of a cubic centimeter.
56.55 = 56.6
Therefore the volume of a hemisphere with a radius of 3cm is 56.6cm^3.
