Question

Answer please!! It's due tomorrow ​

Answer 1

Answer:

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.

Step-by-step 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:

$\tan C = \frac{DF}{CF}$ (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:

$\tan F = \frac{DE}{DF}$ (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:

$\sin Z = \frac{XY}{XZ}$ (3)

($XY = 15$, $Z = 25^{\circ}$)

$XZ = \frac{XY}{\sin Z}$

$XZ = \frac{15}{\sin 25^{\circ}}$

$XZ \approx 35.493$

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

$\tan W = \frac{XZ}{WZ}$ (4)

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

$W \approx \tan^{-1} \left(\frac{22}{35.493}\right)$

$W \approx 31.792^{\circ}$

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:

$\cos \theta = \frac{x}{l}$ (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:

$l = \frac{x}{\cos \theta}$

$l = \frac{6\,ft}{\cos 75^{\circ}}$

$l \approx 23.182\,ft$

The length of the ladder is approximately 23.182 feet.