Answered

Along a long, straight stretch of mountain road with a 7. 2 % grade, you see a tall tree standing perfectly plumb alongside the road. From a point 450 feet downhill from the tree, the angle of inclination from the road to the top of the tree is 6. 2 degrees. Use the Law of Sines to find the height of the tree to the nearest tenth of a foot

Answer :

RAPHEALNWOBIGO

The height of the tree using sine rule is 48.9 feet

The law of sine

The law of sine shows the relationship between the sides and angles of a triangle. It is given by:

a / sinA  = b/sinB = c/sinC

Where A, B, C are the angles and a, b, c are the sides opposite this angles.

Let h represent the height of the tree. The triangle is right angled

The angle opposite the 450 ft distance = 180 - (90 + 6.2) = 83.8°

Hence:

450/sin(83.8) = h/sin(6.2)

h = 48.9 feet

The height of the tree using sine rule is 48.9 feet

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