Question

A Rectangular plane of 100 mm × 50 mm is inclined to H.P. at such an angle that its top view measures 50 mm × 50 mm. Angle of plane with H.P. is​

Answer 1

Given,

Dimensions of a rectangular plane = 100 mm × 50 mm

When the rectangular plane is inclined to a horizontal plane at an angle, its upper view measures = 50 mm × 50 mm

To find,

The angle of the plane with the horizontal plane.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the angle of the rectangular plane with the horizontal plane is x°.

Now, according to the question;

The 50 mm measuring sides of the rectangular plane and the upper view of its inclination are common. An imaginary right-angled triangle is formed whose hypotenuse is formed by the 100 mm measuring side of the rectangular plane and its base is formed by the other 50 mm measuring side of the top view. The acute angle adjacent to the base is equal to x°.

Now,

As per trigonometry, on applying the cosine ratio formula for the angle x, we get;

Cos x = (length of the adjacent base)/(length of the hypotenuse) = 50 mm/100 mm

=> Cos x = 1/2

=> Cos x = Cos 60°

=> x = 60°

Hence, the angle of the plane with the horizontal plane is equal to 60°.