Question

A 30-foot extension ladder leaning against a building makes a 76 degree angle with the ground. How far up the building does the ladder touch?

Answer 1

rsA 30-foot extension ladder leaning against a building makes a 76 degree angle with the ground

Length of ladder = 30 foot

Angle make by ladder with the ground = 76 degree

Let AB represent the length of ladder, AB = 30

OA represent the height of the wall where, ladder touch the wall,

Since, AOB is a right angle triangle,

for angle B = 76,

Hypotenuse = 30, side opposite to angle 76 = OA

From the trgnometric ratio,

`\begin{gathered} \sin \theta=\frac{Opposite\text{ SIde}}{Hypotenuse} \\ \text{ Substitute the value as, }\theta=76,\text{ Hypotenuse }AB\text{ = 30, OA } \\ \sin 76=(OA)/(AB) \\ OA=AB\sin 76 \\ OA=30(\sin 76) \\ OA=30(0.970) \\ OA=29.1 \end{gathered}`

Height of the wall = 29.1 feet

Answer : 29.1 feet

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