Question

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

Answer 1

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.