Mathematics, 18.06.2021 14:00, pokry3814

Answer please!! It's due tomorrow

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answered: almavaldez45

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.

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

- 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.

answered: Guest

typically if you want , you would actually put questions here for us to you. but hey, that's just me. maybe someone will magically answer the questions for you without knowing what they are.

answered: Guest

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!