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kirza4 [7]
3 years ago
11

Bob uses a 20 foot ladder to paint a section of his house that is 16 feet high.

Mathematics
1 answer:
Semenov [28]3 years ago
5 0

Answer:

Option (2) and Option (4)

Step-by-step explanation:

From the picture attached,

Length of ladder AC = 20 feet

Height of the highest point of the ladder from ground AB = 16 ft

By Pythagoras theorem,

AC² = BC² + AB²

BC² = AC² - AB²

BC = \sqrt{(20)^2-(16)^2}

     = \sqrt{400-256}

     = \sqrt{144}

     = 12

Now, Sinθ = \frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{\text{AB}}{\text{AC}}

                 = \frac{16}{20}

Cosθ = \frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{\text{BC}}{\text{AC}}

         = \frac{12}{20}

tanθ = \frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{\text{AB}}{\text{BC}}

        = \frac{16}{12}

Therefore, Option (2) and Option (4) are the correct options.

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