18 a) 6.34ft
We draw a triangle scaled 1cm = 2ft and label 6.34ft 13.57ft x 15ft
b) 11.54 degree
Step-by-step explanation:
a) sin (25) = 0.4226182617 then use as multiplier.
0.4226182617 x 15 = 6.339273926
To find third measurement for use of diagram
we do pythagoras
c^2 - a^2 = b^2 (we are looking for base so b or a applies just stick to one of the c-b or c^2-a^2 = b^2 etc.
c^2 = 15 x 15 = 225
b^2 = 6.339273926 x 6.339273926 = 40.18639391
a^2 = √225 -√40.189 = √184.811
a = 13.57133007
a= 13.57feet to help diagram length we scale 6.34ft x 13.57ft x 15ft slope.
18b) We divide the measurements run/rise always
4/20 = 0.2
Then input them for shift sin-1 (0.2) =11.53695903
Just realised you needed number 20. Hope 18 a+b helps.
With the answer for question 20 you can check the angle of elevation in reminder to my answers on your last page .
run/rise we have 350/ slope = (x 0.57) = shift sin-1 (0.57) = 35 degree we know we are correct as cos also finds this same inverse degree angle of elevation of 55 degree as both add up to 90 degree.
We find pythagoros with a^2 +b^2 = c^2
350sq + 505sq = √122500 + √255025 = √377525
c^2 = √377525 = 614.43 feet for diagrams slope
run/rise = 505/614.43 = 0.82189997233 = 0.82
shift cos-1 (0.82) = 34.91 = 35 degree
We know now that run/rise we should use to check is Sin-1 but cos -1 checks the 35deg+55deg+90 deg = 180 degree as well as checks the other or both inverse angles.
Therefore 505 feet is correct.
