diagonal strut of a rectangular gate is 4.3 meters long the strut makes an angle of 61' 33" with the base side of the gate, find the height of the gate .

Question

 Rectangular gate 4.3 m

Makes an angle of 61degrees 33" with the base

What is the height of the gate in decimal

Answer 1

If you draw a picture of the gate, there is a right triangle formed by the diagonal strut, the base, and the height. The angle is between the base and the diagonal, so the base is adjacent, and the height is the opposite side. You know the diagonal (hypotenuse) and want the height (opposite), so you should use sine to solve.

 

sin (61º33') = h / 4.3 m

h = 4.3 sin (61º33')

 

Plug into your calculator and solve.