Question

The Angle Between A Line And A Plane: Find the angle between the following line segments and the base plane of the figure

Answer 1

1) The angle formed by QR and the base is shown below

The above triangle is a right angle triangle. The angle between QR and the base is #. We would find # by applying the tangent trigonometric ratio which is expressed as

tan # = opposite side/adjacent side

From the triangle,

opposite side = 1

adjacent side = 0.6

tan # = 1/0.6 = 1.67

# = tan^-1(1.67)

# = 59.09

The angle between segment QR and the base is 59.09 degrees

ii) The angle formed by QU and the base is shown below

We would find QU by applying pythagorean theorem which is expresses as

hypotenuse^2 = opposite side^2 + adjacent side^2

Thus, we have

`\begin{gathered} QR^2=1^2+0.6^2\text{ = 1.36} \\ QR\text{ = }\sqrt[]{1.36\text{ }}\text{ = 1.17} \end{gathered}`

We would find # by applying the tangent trigonometric ratio again. Thus, we have

Tan # = 1.17/24 = 0.04875

# = tan^-1(0.04875)

# = 2.79

The angle between line segment QU and the base is 2.79 degrees

iii) The angle formed between line segment QN and the base is shown below

We would find # by applying the tangent ratio again. This, we have

tan # = 1/24 = 0.04167

# = tan^-1(0.04167)

# = 2.39

The angle formed between line segment QN and the base is 2.39 degrees