Cesar is building a shelf at an angle so that it appears to be leaning against the wall. The shelf touches the wall 7 ft. above the floor and the distance between the floor from the wall to the front of the shelf is 1.5 ft. What is the angle the shelf makes with the floor?

A. 77.9 degrees.
B. 77.6 degrees.
C. 12.1 degrees.
D. 12.4 degrees.

A 15-ft. building casts a shadow of 12 ft. What is the approximate angle of inclination of the sun?

A. 51.3 degrees.
B. 53.1 degrees.
C. 36.9 degrees.
D. 19.2 degrees.

1) The problem says:

- The shelf touches the wall 7 feet above the floor.

-The distance between the floor from the wall to the front of the shelf is 1.5 feet

Then:

Tan^-1(α)=Opposite Leg/Adjacent leg

Opposite leg=7
Adjacent leg=1.5

When you substitute the values, you obtain:

Tan^-1(α)=7/1.5
α=77.9°

What is the angle the shelf makes with the floor?

The correct answer is: A) 77.9 degrees.

2) The problem says that the 15-feet building casts a shadow of 12 feet. Then:

Tan^-1(β)=Opposite Leg/Adjacent leg

Opposite leg=15
Adjacent leg=12

When you substitute, you obtain:

Tan^-1(β)=15/12
β=51.3°

What is the approximate angle of inclination of the sun?

The correct answer is: A) 51.3 degrees.

xero099 xero099 · Answer 2 · 2025-04-05T21:58:35-04:00

1) The angle the shelf makes with the floor is approximately 77.905°. (Choice A)

2) The approximate angle of inclination of the sun is approximately 51.340°. (Choice A)

How to apply trigonometric relations to determine angles

1) In this case we know that shelf has a vertical height ([tex]h[/tex]) of 7 feet and a horizontal distance between the floor from the wall to the front of the shelf ([tex]l[/tex]) is 1.5 feet. The angle ([tex]\theta[/tex]), in degrees, is determined by tangent function:

[tex]\theta = \tan^{-1} \frac{7\,ft}{1.5\,ft}[/tex]

[tex]\theta \approx 77.905^{\circ}[/tex]

The angle the shelf makes with the floor is approximately 77.905°. (Choice A) [tex]\blacksquare[/tex]

2) The length of the shadow ([tex]l[/tex]) is 12 feet and the height of the building ([tex]h[/tex]) is 15 feet. The angle of inclination of the sun is determined by tangent function:

[tex]\theta = \tan^{-1} \frac{15\,ft}{12\,ft}[/tex]

[tex]\theta \approx 51.340^{\circ}[/tex]

The approximate angle of inclination of the sun is approximately 51.340°. (Choice A) [tex]\blacksquare[/tex]

To learn more on trigonometric relations, we kindly invite to check this verified question: https://brainly.com/question/6904750