Question

A 10-foot ladder is to be placed Against the side of the building. The base of the latter must be placed in an angle of 72° With the level ground for a secure footing. Find, to the nearest inch, how far the base of the latter should be from the side of the building and how far up the side of the building the latter will reach.

Answer 1

Answer:

Distance of foot of ladder from building: 37.2 inches

Distance of top of ladder from building's base: 114 inches

Step-by-step explanation:

Please refer to the figure attached in the answer area.

A right angled triangle $\triangle ABC$ is formed by the ladder with the building where hypotenuse is the length of ladder.

Hypotenuse, AC = 10 foot

Also, we are given that angle made by the base of ladder with the ground is $72^\circ$.

We have to find AB and BC.

$\angle BAC = 72^\circ$

Using trigonometric functions:

$cos \theta= \dfrac{Base}{Hypotenuse}\\cos 72^\circ= \dfrac{AB}{AC}\\\Rightarrow 0.309 = \dfrac{AB}{AC}\\\Rightarrow AB = 10 \times 0.309\\ \approx 3.1 foot\\ \approx 37.2 inches$

$sin \theta = \dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin72^\circ = \dfrac{BC}{AC}\\\Rightarrow 0.95 = \dfrac{BC}{AC}\\\Rightarrow AB = 10 \times 0.95\\ \approx 9.5 foot\\ \approx 114 inches$

Distance of foot of ladder from building: 37.2 inches

Distance of top of ladder from building's base: 114 inches