Line AC and line DB intersect at point P. Solve for angle BPQ.
1 answer:
You might be interested in
<span>4(2x - 5) = 4
8x - 20 = 4
8x = 4 + 20
8x = 24
x = </span>
x = 3
Part A:
This equation has only one solution. {Working shown above}
Part B:
The solution is x = 3. {Working shown above}
8x - 20 = 4
8x = 4 + 20
8x = 24
x = </span>
x = 3
Part A:
This equation has only one solution. {Working shown above}
Part B:
The solution is x = 3. {Working shown above}
To compute the distance between the points, we can apply the distance formula as shown below.
In which x₁ and x₂ are the x-coordinates and y₁ and y₂ are the y-coordinates of the two points. Thus, applying this with the segments AABB, AACC, and BBCC, we have
Now that we have the lengths of all the sides of ΔAABBCC, we can find the missing angles using the Law of Cosines.
Generally, we have
or
Hence, we have
Simplifying this, we have
Thus, from this, we can arrange the angles from smallest to largest: ∠CC, ∠AA, and ∠BB.
Answer: ∠CC, ∠AA, and ∠BB
In which x₁ and x₂ are the x-coordinates and y₁ and y₂ are the y-coordinates of the two points. Thus, applying this with the segments AABB, AACC, and BBCC, we have
Now that we have the lengths of all the sides of ΔAABBCC, we can find the missing angles using the Law of Cosines.
Generally, we have
or
Hence, we have
Simplifying this, we have
Thus, from this, we can arrange the angles from smallest to largest: ∠CC, ∠AA, and ∠BB.
Answer: ∠CC, ∠AA, and ∠BB