The 1st term in a geometric series is 5 and the common ratio is 2. Find the sum of the 1st 10 terms in the series.
1 answer:
You might be interested in
Answer:
The difference between the greatest and the smallest angle of the triangle PBQ is 98°.
Step-by-step explanation:
The question is:
In a triangle ABC, angle B measures 64 ° and angle C measures 72°. The inner bisector CD intersects the height BH and the bisector BM at P and Q respectively. Find the difference between the greatest and the smallest angle of the triangle PBQ.
Solution:
Consider the triangle ABC.
The measure of angle A is:
angle A + angle B + angle C = 180°
angle A = 180° - angle B - angle C
= 180° - 72° - 64°
= 44°
It is provided that CD and BM are bisectors.
That:
angle BCP = angle PCH = 36°
angle CBQ = angle QBD = 32°
angle BHC = 90°
Compute the measure of angle HBC as follows:
angle HBC = 180° - angle BHC + angle BCH
= 180° - 90° - 72°
= 18°
Compute the measure of angle BPC as follows:
angle BPC = 180° - angle PCB + angle CBP
= 180° - 18° - 36°
= 126°
Then the measure of angle BPQ will be:
angle BPQ = 180° - angle BPC
= 180° - 126°
angle BPQ = 54°
Compute the measure of angle PBQ as follows:
angle PBQ = angle B - angle QBD - angle HBC
= 64° - 32° - 18°
angle PBQ = 14°
Compute the measure of angle BQP as follows:
angle BQP = 180° - angle PBQ - angle BPQ
= 180° - 14° - 54°
angle BQP = 112°
So, the greatest and the smallest angle of the triangle PBQ are:
angle BQP = 112°
angle PBQ = 14°
Compute the difference:
<em>d</em> = angle BQP - angle PBQ
= 112° - 14°
= 98°
Thus, the difference between the greatest and the smallest angle of the triangle PBQ is 98°.
<h3>Answer: 2.2 units</h3>
============================================
Explanation:
I'll define these point labels
- B = Blake's starting position
- F = finish line
- C = the third unmarked point of the triangle
The locations of the points are
- B = (-8,1)
- C = (-6,-3)
- F = (4,-2)
Use the distance formula to find the distance from B to C
Segment BC is roughly 4.47214 units long.
Following similar steps, you should find that segment CF is approximately 10.04988 units long.
If Blake doesn't take the shortcut, then he travels approximately BC+CF = 4.47214+10.04988 = 14.52202 units. This is the path from B to C to F in that order.
---------
Use the distance formula again to find the distance from B to F. This distance is about 12.36932 units. He travels this amount if he takes the shortcut.
Subtract this and the previous result we got
14.52202 - 12.36932 = 2.1527
That rounds to 2.2
This is the amount of distance he doesn't have to travel when he takes the shortcut.
In other words, the track is roughly 2.2 units shorter when taking the shortcut.
Side note: Replace "units" with whatever units you're working with (eg: feet or meters).