Question

Answer please!! It's due tomorrow ​

Answer 1

15) The length of the line segment DE is 14.908.

16) The measure of the angle W is approximately 31.792°.

17) The length of the ladder is approximately 23.182 feet.

Explanation:

15) We present the procedure to determine the length of segment DE:

(i) Determine the length of the line segment DF by trigonometric relations:

`\tan C = (DF)/(CF)` (1)

(
`C = 61^(\circ)`,
`CF = 24`)

`DF = CF\cdot \tan C`

`DF = 24\cdot \tan 61^(\circ)`

`DF \approx 43.297`

(ii) Determine the length of the line segment DE by trigonometric relations:

`\tan F = (DE)/(DF)` (2)

(
`DF \approx 43.297`,
`F = 19^(\circ)`)

`DE = DF\cdot \tan F`

`DE = 43.297\cdot \tan 19^(\circ)`

`DE \approx 14.908`

The length of the line segment DE is 14.908.

16) We present the procedure to determine the measure of the angle W:

(i) Determine the length of the line segment XZ by trigonometric relations:

`\sin Z = (XY)/(XZ)` (3)

(
`XY = 15`,
`Z = 25^(\circ)`)

`XZ = (XY)/(\sin Z)`

`XZ = (15)/(\sin 25^(\circ))`

`XZ \approx 35.493`

(ii) Calculate the measure of the angle W by trigonometric relations:

`\tan W = (XZ)/(WZ)` (4)

(
`XZ \approx 35.493`,
`WZ = 22`)

`W \approx \tan^(-1) \left((22)/(35.493)\right)`

`W \approx 31.792^(\circ)`

The measure of the angle W is approximately 31.792°.

17) The system form by the ladder, the ground and the wall represents a right triangle, whose hypotenuse is the ladder, which is now found by the following trigonometric relation:

`\cos \theta = (x)/(l)` (5)

Where:

`\theta` - Angle of the ladder above ground, in sexagesimal degrees.

`x` - Distance between the foot of the ladder and the base of the wall, in feet.

`l` - Length of the ladder, in feet.

If we know that
`x = 6\,ft` and
`\theta = 75^(\circ)`, then the length of the ladder is:

`l = (x)/(\cos \theta)`

`l = (6\,ft)/(\cos 75^(\circ))`

`l \approx 23.182\,ft`

The length of the ladder is approximately 23.182 feet.