Answer:
18a) The height of tree is 6.34ft.
Diagram We would scale a right side triangle showing side; 6.34ft x base 13.59ft x 15cm slope.
b) 11.54 degree
Explanation:
18a) sin(25) = 0.4226182617 is what you multiply to check the height.
15 x 0.4226182617 = 6.339273926 = 6.34ft.
Using the measurements of pythagoras you can scale each measurement above. 6.34 = (x0.5) = 3.17cm to draw the trees height.
15ft wire = scale the diagram draw 1cm = 2ft So that 7.5cm = = 15ft
Draw a right angle triangle and before creating the slope use protractor or guess 25 degree at bottom of slope and label it.
This will make a 7.5cm slope and label it 15ft.
We also measure out the base which on scale cm per foot is 13.59 x 0.5 = 6.80cm and label it 13.59ft.
We find the base measurement by finding the square of each 15 and 6.34
c^2 - a^2 = b^2
a= 6.34 x 6.34 = 40.1863939089 = √40.19
c = 15 x 15 = √225
c-b = √225 - √40.19 = √184.81
side = b
b^2 = √184.81= 13.5944841756 = 13.59ft
18 b) To find an angle x with given measurements 4ft base and 20ft slope we
use sin( base/slope) = (run/rise)
So that 4/20 = 0.2
Then plug in for sin -1 0.2 = 11.54 degree = (calc ..11.53695903)
Notes;
If 4ft base was not given and the height of wall was given we would do the same using base as run and slant as run run/rise but we would substitute sin-1 and after division run/rise we would plug in the decimal to cos-1 (decimal).