3D trigonometry as in picture

(a)

9.11

(b)

70.8

Step-by-step explanation:

(a)

We can find AG by finding AC and CG, then using the Pythagorean Theorem. To find AC, awe can create triangle ABC, using the Pythagorean Theorem to find AC=√(5²+7²)≈8.602. Since this is a cuboid, CG=AE=3, as the height is constant. Therefore, √(AC²+3²)=AG=9.11, rounded to 3 significant figures.

(b)

To find this, we can create triangle AGC, finding angle G. This is because CG is directly on the plane, and this is the angle that goes right next to that line. Therefore, cos(G)=3/9.11, and G=arccos(3/9.11)=around 70.8

50-60=10

step-by-step explanation:

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!