A tree casts a shadow of 27 meters when the angle of elevation of the sun is 26 degrees. Find the height of the tree to the nearest meter.
a. 24 m
b. 15 m
c. 320 m
d. 13 m
A. 38.36
B. 17.85
C. 20 02
D. 26.25
Then, what is the answer
To find the height of the tree, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.
Let's denote the height of the tree as 'h' and the distance from the tree to the end of its shadow as 'd'.
From the given information, we know that the length of the shadow (opposite side) is 27 meters, and the angle of elevation (the angle between the ground and a line from the ground to the top of the tree) is 26 degrees.
Using the tangent function, we have:
tan(26°) = h/d
Rearranging the formula, we get:
h = d * tan(26°)
To find the height, we need to determine the value of 'd'. Since the length of the shadow is 27 meters, 'd' is also equal to 27 meters.
Plugging in the values into the formula:
h = 27 * tan(26°)
Using a calculator, we find:
h ≈ 13 meters
Therefore, the height of the tree is approximately 13 meters. The correct answer is option d.
To find the height of the tree, we can use trigonometry. The shadow of the tree, the height of the tree, and the angle of elevation of the sun form a right triangle.
Let's label the height of the tree as 'h' and the length of the shadow as 's'. The angle of elevation of the sun, which is the angle between the ground and the sun's rays, is given as 26 degrees.
Using the trigonometric function tangent (tan), we have the equation: tan(angle) = opposite/adjacent.
In this case, the opposite side is the height of the tree 'h', and the adjacent side is the length of the shadow 's'.
So, tan(angle) = h/s
Rearranging the equation, we have: h = s * tan(angle)
Substituting the given values, we have: h = 27 * tan(26)
Calculating the value using a calculator, we get: h ≈ 12.9387
To the nearest meter, the height of the tree is approximately 13 meters.
Therefore, the correct option is d. 13 m.
let x = height of tree
tan(angle) = x/27
tan(26) = x/27
x = 0.488*27
x = 13.17 = 13 m