Sally was standing 30 feet from a tree. The angle of

elevation from her eyes (4 feet above the ground)

to the top of the tree was 38°. How tall is the tree?

Round your answer to the nearest foot.

Explain your steps

The tree was 27 feet tall

Step-by-step Explanation: First of all Sally was standing 30 feet away from the tree and she looks up at an angle of elevation of 38 degrees to the top of the tree. With this bit of information we can determine that a right angled triangle has been formed with the reference angle as 38 degrees, the side facing it as h (the height of the tree) and the adjacent side as 30. We shall apply the trigonometric ratio as follows;

Tan 38 = opposite/adjacent

Tan 38 = h/30

0.7813 = h/30

0.7813 x 30 = h

23.4 = h

We remember at this point that Sally’s eyes were 4 feet above the ground. What we have just calculated is the height of the tree from “4 feet above the ground” (where her eyes were). Hence the actual height of the tree is calculated as 23.4 plus 4 which gives us 27.4

Therefore the tree was 27 feet tall (approximately to the nearest foot)

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