A tree casts a shadow 9.3.m long when the angle of the sun is 43°. How tall is the tree?

1 Answer
Apr 6, 2018

The tree is about #color(blue)("8.67 meters"# tall.

Explanation:

#" "#
Examine the image below:

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The tree's shadow (AB) is #"9.3 meters"# long.

From the location B, the sun is at an angle of is #43^@#.

Our objective is to find the height of the tree (AC)

We are given angle #43^@#.

Side opposite to this angle is #AC#, which is the height of the tree.

Side adjacent to this angle is #AB#

The formula which connects these three known values is:

#tan(/_ABC) = # Opposite Side#/# Adjacent Side.

#rArr tan(43^@) = (AB)/(BC)#

#:. AB = tan(43^@)*BC#

Using the calculator, #tan(43^@) ~~ 0.9325#

So,

#AB~~(0.9325)*(9.3)#

#AB~~8.67239# meters.

Hence, the tree is about #color(blue)("8.67 meters"# tall.

Hope you find this solution useful.