A fireman has 12 ft. ladder and a 16 ft ladder. He leans the 12 ft ladder against a house at an angle of 57 degrees. He leans the 16 ft ladder against a house 30-degree angle. Which ladder will he climb to the higher height? Explain you answer

12 feet ladder

Step-by-step explanation:

Height of 12 ft ladder :

Using Pythagoras :

Tan θ = Adjacent / hypotenus

Tan 57 = h / 12

1.5398649 * 12 = 18.48 feets

For 16 feet ladder :

Tan θ = Adjacent / hypotenus

Tan 30 = h / 16

0.5773502 * 16 = 9.24 feets

18.48 > 9.24

Hence, he'll climb the 12 feets ladder to the higher height

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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