The angle of elevation to the top of a particular skyscraper in New York is found to be 12 degrees from the ground at a distance of 1.3 mi from the base of the building. Using this information, find the height of the skyscraper. * 20 points a. 1560 ft b. 2918 ft c. 1459 ft

The height of the skyscraper is 1,459 ft. Choice c

Step-by-step explanation:

Right Triangles

The ground and the building form a right angle (90°). In the right triangles, the trigonometric ratios are satisfied. To solve the problem we use the tangent ratio, defined as:

The angle of elevation from which the skyscraper can be seen is θ=12°. The opposite side of this angle is the height of the skyscraper H and the adjacent side is the distance from the ground X=1.3 miles.

Converting miles to feet: X=1.3*5,280 = 6,864 ft

Applying the tangent ratio to the angle of elevation:

Solving for H:

Calculating:

H = 1,459 ft

The height of the skyscraper is 1,459 ft. Choice c

5104.38 inches

step-by-step explanation:

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5