Solve each problem graphically on engineering paper then che

Solve each problem graphically on engineering paper then check mathematically. A right triangle has a hypotenuse length of 52 inches an angle of 52 . What are the measurements for the 3rd angle and the length of the two legs? Check your answer mathematically. Draw a right triangle that has leg measurements of 41 mm and 26 mm. From your drawing, measure the length of the hypotenuse and the two unknown angles. Check your answer mathematically. Recreate the drawing below using a scale of 1:1. Lengths of sides AB = 3.00\" & BC = 5.00\" and internal angles A=84 degree, B=114 degree, C=77 degree. What are measurements of sides CD & DA and the internal angle at point D? Check your answers mathematically.

Solution

1. We can only show the mathematical proof here:

Right Angled Triangle: Hypo = 52 inch ; Angle 52 deg

Base = 52*cos52 = 32

Height = 52sin52 = 41

The third angle = 180 -90 -52 = 38 deg

2. Leg measurements of Righ Angled Triangle = 41mm and 26 mm

Hypotenuse = sqrt( 41^2 +26^2) = 48.54

Base angle x : tanx =(41/26) =1.5769

x = 57.62 deg

Third Angle = 180 -90 -57.62 = 32.38 deg