Answer:
Q2) 29 degree as unrounded to nearest degree is 28.95 degree
Q3) 69 degree as unrounded to nearest degree is 68.56 degree
Step-by-step explanation:
QU 2)
When they speak of plane we see ABCD and also see ABC
So we need the length of AB and BC to find the diagonal CA
AB^2 + BC^2 = CA^2
16.4^2 + 9.1^2 = sqrt 351.77
CA^2 = sqrt 351.77 = 18.8 cm
We know CG = 10.4cm
We identify the hypotenuse for ACG triangle
We do trig tan x = opp/adj for CGA angle
Tan x = tan-1 10.4/18.8 = 28.95099521 degree
Tan x = tan-1 18.8/10.4 = 61.04900479 degree
so we know one is much smaller than the other
We also know ACG angle is 90 degree and that angle from ABCD that meets line AG is the smaller angle.
Answer therefore must be 28.95 degree = or 29 degree
QU 3)
we are basically looking for angle where VB meets BC line or AVB meets ABC we have the slant length, so step 1 is find the height by first dividing square base by 2 then finding the height.
= 7.6/2 = 3.8 cm
Then Pythagoras
BV^2 - 1/2 BC = height
10.4^2 - 3.8^2 = height
Height = sq rt 93.72 =9.68090905 = 9.7cm
Which means V to midpoint VC = V to midpoint AB
They are the same and the midpoints are 90 degree angles.
To find the required angle for VB + BCmidpoint or we wont be able to determine the right angle hypotenuse.
We do the same as last question determine the hypotenuse and where the angle sought is is where we use the trig function = adj/hyp
Because if it was the midpoint angle then it would be opp/adj like the question 1 so this time its cos of x.
cos x = adj/hyp = cos-1 (3.8/ 10.4) = 68.5687455
Answer is 68.56 degree
The reason we show the height is so we can check by doing opp/hyp
= sin of x = sin-1 (9.68090905/3.8) = 23.11171135
and 90 -23.11171135 = 66.8882887
= 67 degree
So we go with the first one and assume 9.68 was already simplified to 9.7cm
= sin-1 (3.8/9.7) = 23 degree 90-23 = 67 degree
but when rounded to 10.4cm for slant we get the same
= sin-1 (3.8/10.4)
So we realise here trig functions -1 doesn't work on the same 90 degree angle for both lines that meet such 90 degree angle.
We try the sin-1 (10.4/ 9.68090905) = 68.5687455 = 69 degree
and that where the lines join away from the 90 degree angle we can always find true answer, and see it is a match with the first cos trig function we did.
This proves that cos line 1/line2 = sin line 1/line 2 are the same when the larger number is numerator for sin representing the hypotenuse slant for sin as shown and when the larger of the sides is numerator for cos di
and smallest side acts as denominator for both trig functions.
