In the design of a new building, a doorway is 2.45 ft above the ground. a ramp for the disabled, at an angle of 4.5 ° with the ground, is to be built up to the doorway. how long will the ramp be?

Length of the ramp, l = 31.22 feet

Explanation:

It is given that,

A doorway is 2.45 ft above the ground, AB = 2.45 ft

Angle between the ground and the ramp is,

Applying trigonometry,

AC = 31.22 ft

So, the length of the ramp is 31.22 feet. Hence, this is the required solution.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west