Question

a.
Jamie has a ladder that is 15 ft long. She wants to lean the ladder against a vertical wall so that
the top of the ladder is 14 ft above the ground.
Draw a picture of the ladder leaning against the wall and label the lengths listed in the problem:

b. Use Trigonometry to find the angle formed between the ground and the ladder using your
diagram and values from part 1a. Round to the nearest whole number. Show your work:
c. For safety reasons, Jamie wants the angle of the ladder makes with the ground to be no greater than 75 degrees. Will the ladder be safe the way she has it positioned?

Answer 1

Answer:

(a)Attached

(b)69 degrees

(b)The ladder is safe

Step-by-step explanation:

(a)See attached diagram

The wall is length |AB| and the ladder is length |AC|

(b)

$sin \theta =\dfrac{|AB|}{|AC|} \\sin \theta =\dfrac{14}{15}\\\theta=arcsin (\dfrac{14}{15})\\\theta=69^\circ$

(c)Jamie wants the angle of the ladder makes with the ground to be no greater than 75 degrees for safety reasons.

Since the angle formed between the ground and the ladder (69 degrees) is less than 75 degrees, the ladder is safe the way it is positioned.