Answer:
X=40°
X=30°
X=50°
Step-by-step explanation:
Let our unknown angles be denoted by ![X](https://tex.z-dn.net/?f=X)
Part I
We are given the sum of the angles as 70°, the known as 30° and the unknown as X;
To find X, we subtract the known angle from the sum as:
X=70°-30°=40°
Hence X= 40°
Part II
We are given the sum of the angles as 70°, the known as 40° and the unknown as X;
To find X, we subtract the known angle from the sum as:
X=70°-40°=30°
Hence X= 30°
Part III
We are given the sum of the angles as 80°, the known as 30° and the unknown as X;
To find X, we subtract the known angle from the sum as:
X=80°-30°=50°
Hence X= 50°
Answer:
The road running along the third side was 3 miles long.
Step-by-step explanation:
Given,
Length of hypotenuse = ![5\ mi](https://tex.z-dn.net/?f=5%5C%20mi)
Length of one leg = ![4\ mi](https://tex.z-dn.net/?f=4%5C%20mi)
We have to find the length of the third side.
Solution,
Since the field is in the shape of a right triangle.
So we use the Pythagoras theorem to find the length of the third side.
"In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of other two sides".
On framing in equation form, we get;
![c^2=a^2+b^2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2)
Where 'a' = 1st side of right triangle
'b' = 2nd side of right triangle
'c' = hypotenuse
Now we put the given values and get;
![5^2=4^2+b^2\\\\25=16+b^2\\\\b^2=25-16\\\\b^2=9](https://tex.z-dn.net/?f=5%5E2%3D4%5E2%2Bb%5E2%5C%5C%5C%5C25%3D16%2Bb%5E2%5C%5C%5C%5Cb%5E2%3D25-16%5C%5C%5C%5Cb%5E2%3D9)
Now taking square root on both side, we get;
![\sqrt{b^2} =\sqrt9\\\\b=3\ mi](https://tex.z-dn.net/?f=%5Csqrt%7Bb%5E2%7D%20%3D%5Csqrt9%5C%5C%5C%5Cb%3D3%5C%20mi)
Hence The road running along the third side was 3 miles long.
36+48j 36+48+j hopethishelped