Answer: Explanation and answer is attached.
Step-by-step explanation:
Answer:
6 units
Step-by-step explanation:
Given: Points H and F lie on circle with center C. EG = 12, EC = 9 and ∠GEC = 90°.
To find: Length of GH.
Sol: EC = CH = 9 (Radius of the same circle are equal)
Now, GC = GH + CH
GC = GH + 9
Now In ΔEGC, using pythagoras theorem,
......(ΔEGC is a right triangle)





Now, Let GH = <em>x</em>

On rearranging,




So x = 6 and x = - 24
∵ x cannot be - 24 as it will not satisfy the property of right triangle.
Therefore, the length of line segment GH = 6 units. so, Option (D) is the correct answer.
Answer: The distance between the girls is 362.8 meters.
Step-by-step explanation:
So we have two triangle rectangles that have a cathetus in common, with a length of 160 meters.
The adjacent angle to this cathetus is 40° for Anna, then the opposite cathetus (the distance between Anna and the tower) can be obtained with the relationship:
Tan(A) = opposite cath/adjacent cath.
Tan(40°) = X/160m
Tan(40°)*160m = 134.3 m
Now, we can do the same thing for Veronica, but in this case the angle adjacent to the tower is 55°
So we have:
Tan(55°) = X/160m
Tan(55°)*160m = X = 228.5 m
And we know that the girls are in opposite sides of the tower, so the distance between the girls is equal to the sum of the distance between each girl and the tower, then the distance between the girls is:
Dist = 228.5m + 134.3m = 362.8m
Step-by-step explanation:
-7y > 161
7y < 161
7÷7=1
161÷7=23
y=23
7y > -161
7÷7=1
-161÷7=-23
y=-23