Final answer:
To determine the height of a tree with a 60-degree angle of elevation and a 10-meter shadow, the tangent function from SOHCAHTOA is used, giving the height as 10√3 meters. Option C) is correct.
Step-by-step explanation:
To solve the SOHCAHTOA question related to a tree's shadow, we have to apply trigonometry to find the height of the tree. The acronym SOHCAHTOA helps us remember the definitions of sine (sin), cosine (cos), and tangent (tan). We know that the tree's shadow is 10 meters and the angle of elevation of the sun is 60 degrees.
Using the tangent function (tan) which is the opposite side over the adjacent side (TOA), and knowing the angle and the length of the shadow (adjacent side), we can write the following equation:
tan(60 degrees) = height of tree / 10 meters
Solving this, we have:
height of tree = 10 meters * tan(60 degrees)
Since tan(60 degrees) equals sqrt(3), the equation becomes:
height of tree = 10 meters * sqrt(3)
The height of the tree is therefore 10√3 meters.
Thus, the correct option is C) 10√3 meters.