Help me find the Angle

Find Angle ECB

========================================================

Step 1) Find angle EDC. This is the missing acute angle of the right triangle. Let's call this angle x for now. This angle x adds to the other acute angle (31) to get 90, so 31+x = 90 which solves to x = 59 when you subtract 31 from both sides.

Step 2) Add angles EDC and ADE to get 59+60 = 119. So angle ADC is 119 degrees.

Step 3) Using the idea that adjacent angles of a parallelogram are supplementary, we add adjacent angles ADC and BCD to get 180. Let y be the measure of angle BCD. So we have 119+y = 180 which solves to y = 61

Step 4) Let z be the measure of angle ECB. This adds to angle ECD = 31 to get the measure of angle BCD. So, z+31 = 61 solves to z = 30

Check out the diagram below.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,