Question

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Answer 1

The length of ladder is 15 ft

The ladder is making an angle of 52 degree with the base, with the help of the building

Where, the building and the base are perpendicular to each other i.e. makes an angle of 90

Thus, we have right angle triangle : AOB

Since, we need to find the base length of the triangle i.e. BO

Apply the trignometric ratio of Cosine of angle :

`\cos \theta=\frac{Adjacent\text{ Side}}{\text{Hypotenuse side}}`

In the given triangle for angle B = 52 degree, Adjacent side of angle B is BO and the hypotenuse side is AB

Substitute the value in the expression of cosine :

`\begin{gathered} \cos \theta=\frac{Adjacent\text{ Side}}{\text{Hypotenuse side}} \\ \cos 52=(BO)/(AB) \\ \cos 52=(BO)/(15) \\ \text{Apply cross multiplication :} \\ BO\text{ = 15 (Cos52)} \\ BO=15(0.6156) \\ BO=9.234 \\ To\text{ the nearest tenths} \\ BO=9.2\text{ ft} \end{gathered}`

As, BO express the base of triangle AOB

such that BO is the distance between the Base of the building and the ladder

Thus, Distance between the base of ladder and the building is 9.2 ft

Answer : Distance between the base of ladder and the building is 9.2 ft