+1904 From the ledge of a cliff, Yousif sees a church steeple \(22860\) meters away from the base of the cliff. If Yousif sees the church steeple at a depression of 42° 35' 23", how tall, in yards, is the cliff? Round your answer to the nearest thousandth and write the answer in a complete sentence. Note: 1 meter is equal to 0.9144 yards.
+1904 First convert \(42° 35' 23"\) from degrees minutes and seconds to degrees
\(42° + 35/60°+23/3600°\)
\(42.5833333333333333...°+23/3600°\)
\(42.5897222222222222...°\)
Subtract answer from 90° to find the angle of the side opposite the cliff to the ground
\(90°-42.5897222222222222...°\)
\(47.4102777777777777...°\)
Find the height of the cliff
Let x = height of the cliff
\(tan(\Theta)=opposite/adjacent \)
\(tan(47.4102777777777777...°)=x/22860\)
\(tan(47.4102777777777777...°)*22860=x\)
\(x=tan(47.4102777777777777...°)*22860\)
\(x= 1.087883430651...°*22860\)
\(24869.01522468186...\) meters
Change meters to yards
\(24869.01522468186*.9144\)
\(22740.227521449092784...\) yards
The height of the cliff Yousif is standing on the edge of is approximately 22740.228 yards.
