Mathematics, 31.07.2019 19:30, kandikisses2101

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.

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answered: kadenreynolds5

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 () of 7 feet and a horizontal distance between the floor from the wall to the front of the shelf () is 1.5 feet. The angle ( $\theta$ ), in degrees, is determined by tangent function:

$\theta = \tan^{-1} \frac{7\,ft}{1.5\,ft}$

$\theta \approx 77.905^{\circ}$

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

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

$\theta = \tan^{-1} \frac{15\,ft}{12\,ft}$

$\theta \approx 51.340^{\circ}$

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

To learn more on trigonometric relations, we kindly invite to check this verified question: link

answered: brendaandrade1889

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.

answered: Guest

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

Which are the possible side lengths of a triangle?

answered: Guest

answer: it's upside down and i can't read it

step-by-step explanation:

Me with this . im really bad at these types of problems!

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Cesar is building a shelf at an angle so that it appears to be leaning against the wall. the shelf t...