From two points X and Y, the angles of elevation of the top (T) of a church TZ are 14 degrees and 19 degrees respectively. If XYZ is a horizontal straight line and XY- 120m, find YT and the height of the tower
Draw/sketch a triangle with base 120 and angles 14 and 19 on the base and the other angle is 180-33=147.
Draw a vertical line for the tower. Call height x.
You have 2 right angle triangles now so you can find 2 angles at the top (76 and 71).
Call vertical height x
Call 2 base lengths p and q where p+q=120
Then use sin, cosine, tangent rules to find lengths.I've no calculator with me with sines etc so I can't do it for you.
you'll need to use substitutions
Use the sine rule to calculate YT. Angle TXY is 14deg, angle TYZ is 19 deg, so angle YTX is 5 deg (exterior angle of triangle). YT/sin14 = 120/sin5, i.e. YT=120 sin14/sin 5.
Then TZ/TY is sin19, so TZ=TYsin19 =120*sin14*sin19/sin5