Question

you are standing looking at a large painting on the wall. the bottom of the painting is 1 foot above your eye level. The painting is 10 feet tall. assume you are standing x feet from the painting and that angle theta is formed by the lines of vision to the bottom and to the top of the painting.
If you are standing 10 feet from the painting then what is angle theta

Answer 1

Answer:

1. Height of the painting (h) = 10 feet.
2. Distance of painting from you (d) = 10 feet.

Therefore,

In the formed triangle,

tan theta = h/d

tan theta = 10/10

tan theta = 1

Therefore,

tan theta = 1 = tan 45°

or,

theta = 45°

Therefore, the value of theta is 45° ans.

Answer 2

The value of theta would be $\theta = tan^{-1} (\frac{11}{10})$

Step-by-step explanation:

It is given that:

• The height of the given painting $= 10 ft$
• The distance between the bottom of the painting and the eye level $= 1 ft$

Thus, the total vertical distance between the eye level of the person and the top of the painting $= 10 +1 = 11 ft$

• The horizontal distance between the painting and the person $= 10 ft$

To find the angle theta, we can use the tangent (tan) relation.

• tan theta = $tan\theta =\frac{ perpendicular}{base} = \frac{11}{10}$
• Hence, the value of theta would be $\theta = tan^{-1} (\frac{11}{10})$