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:
(1)
(,
)
(ii) Determine the length of the line segment DE by trigonometric relations:
(2)
(,
)
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:
(3)
(,
)
(ii) Calculate the measure of the angle W by trigonometric relations:
(4)
(,
)
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:
(5)
Where:
- 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 and
, then the length of the ladder is:
The length of the ladder is approximately 23.182 feet.