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,
[tex]\begin{gathered} \sin \theta=\frac{Opposite\text{ SIde}}{Hypotenuse} \\ \text{ Substitute the value as, }\theta=76,\text{ Hypotenuse }AB\text{ = 30, OA } \\ \sin 76=\frac{OA}{AB} \\ OA=AB\sin 76 \\ OA=30(\sin 76) \\ OA=30(0.970) \\ OA=29.1 \end{gathered}[/tex]Height of the wall = 29.1 feet
Answer : 29.1 feet
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