Question
Asked Sep 23, 2019

On level ground, you stand 27.0 m from the base of a tree and determine that the treetop is at 42  degrees  above the horizontal, as measured from ground level.  How do you figure out how tall the tree is conceptually?

check_circleExpert Solution
Step 1

Consider the following diagram, which represents the situation mentioned in the question. Here, AB is the tree’s height and AC is the distance of base of the tree from the observing person such that the angle ACB is equal to 42 degrees. Note that the triangle BAC forms a right triangle.

В,
42°
С
А
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В, 42° С А

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Step 2

Use the trigonometric expression for the tangent of an angle to write the tangent of the angle ACB as,

AB
tan (ZACB)
AC
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AB tan (ZACB) AC

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Step 3

Here, AB is the perpendicular length and AC is the base length for the a...

AB (AC) tan (ZACB)
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AB (AC) tan (ZACB)

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