Answer:
1. The ladder forms 71.8° with the ground.
2. The top of the ladder will reach 18.79 feet up the wall.
3. Height = 8.66 cm and area = 21.65 sq. cm.
Step-by-step explanation:
1. If the angle of elevation of the ladder is [tex]\theta[/tex] then we can write
[tex]\sin \theta = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{19}{20}[/tex]
⇒ [tex]\theta = \sin ^{-1}(\frac{19}{20}) = 71.8[/tex] Degrees.
Therefore, the ladder forms 71.8° with the ground. (Answer)
2. Now, if the ladder formed a 70 degree angle with the ground and the length of the ladder remains the same as 20 feet, then we can write
[tex]\sin 70 = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{x}{20}[/tex]
⇒ x = 20 sin 70 = 18.79 feet.
Therefore, the top of the ladder will reach 18.79 feet up the wall.
3. See the attached figure.
We have, [tex]\tan 60 = \frac{BC}{CD} = \frac{BC}{5}[/tex]
⇒ Height = BC = 5 tan 60 = 8.66 cm.
Therefore, the area of the triangle BCD will be = [tex]\frac{1}{2} \times CD \times BC = \frac{1}{2} \times 5 \times 8.66 = 21.65[/tex] sq. cm. (Answer)
