A tree has a shadow of 12m. If the sun's rays strike the ground at an angle of 27 degrees, how tall is the tree?
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Turn this information into a triangle. The tree and the ground make a 90-degree angle. The sun's rays and the ground make a 27-degree angle. That means that the angle made by the sun and the tree is 63 degrees, because 180 - 90 - 27 = 63 (the sum of the angles of a triangle must always equal 180 degrees).
Now I'm going to set this up by labeling the three angles of the triangle (27, 63, and 90) with an uppercase letter (A, B, and C) and labeling the corresponding sides (the side across from the angle in the triangle) with a lowercase letter (a, b, and c).
A = 27
B = 63
C = 90
a = ?
b = 12m
c = ?
You are looking for side a, the height of the tree, which is opposite of the 27-degree angle. You can find this by using the Law of Sines, which is a/sinA = b/sinB
Substitute in your data: a/sin27 = 12/sin63
12 x sin27 = 11.4765111
11.4765111/sin63 = 68.5755614
The height of the tree is about 68.6m.
Now I'm going to set this up by labeling the three angles of the triangle (27, 63, and 90) with an uppercase letter (A, B, and C) and labeling the corresponding sides (the side across from the angle in the triangle) with a lowercase letter (a, b, and c).
A = 27
B = 63
C = 90
a = ?
b = 12m
c = ?
You are looking for side a, the height of the tree, which is opposite of the 27-degree angle. You can find this by using the Law of Sines, which is a/sinA = b/sinB
Substitute in your data: a/sin27 = 12/sin63
12 x sin27 = 11.4765111
11.4765111/sin63 = 68.5755614
The height of the tree is about 68.6m.