SOLUTION: A tower stands vertically on sloping ground whose inclination with the horizontal is 13 degrees. From a point 40.0m downhill from the tower (measured along the slope) the angle

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Question 42271: A tower stands vertically on sloping ground whose inclination with the horizontal is 13 degrees. From a point 40.0m downhill from the tower (measured along the slope) the angle of elevation of the top of the tower is 20 degrees. How tall is the tower?
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!

Let CD be the tower on the inclined plane AC.
Inclination of AC with ground is 13%5Eo is < BAC = 13%5Eo.
Angle of elevation of the top of the tower is 20%5Eo from the point A which is at a distance of 40 m along the inclined plane from the base C of the tower.
So < CAD = 20%5Eo and AC = 40 m.
So < BAD = < BAC + < CAD = 13%5Eo+%2B+20%5Eo = 33%5Eo

In right-angled triangle ABC,
AB%2FAC+=+cos%2813%5Eo%29
or AB+=+AC%2Acos%2813%5Eo%29
or AB+=+40%2Acos%2813%5Eo%29 _____(1)

In right-angled triangle ABD,
BD%2FAB+=+tan%2833%5Eo%29
or BD+=+AB%2Atan%2833%5Eo%29
or BD+=+40%2Acos%2813%5Eo%29%2Atan%2833%5Eo%29 [from (1)]

Also, in right-angled triangle ABD,
BC%2FAC+=+sin%2813%5Eo%29
or BC+=+AC%2Asin%2813%5Eo%29
or BC+=+40%2Asin%2813%5Eo%29

Height of the tower = CD = BD - BC
= 40%2Acos%2813%5Eo%29%2Atan%2833%5Eo%29+-+40%2Asin%2813%5Eo%29
= 16.31

Hence, the reqd. height of the mountain is 16.31 m.