if im standing 28 meters from a tree....the tree is leaning 7 degrees vertically away from u...the degree of elevation is 26 degrees from feet to tree...whats the height of the tree?
Draw a diagram. For example:
http://img33.imageshack.us/img33/5981/1260158305.png
You have a triangle in which all three angles are known, together with one of the sides.
Use the sine rule to solve for the height of the tree. First solve for L, the side of the triangle opposite the 26° angle using
L/sin(26°) = 28/sin(57°)
The height, H of the tree is
H = L*cos(7°).
I get less than 15m for H.
To find the height of the tree, we can use trigonometric functions. The given information allows us to form a right-angled triangle. Here's how:
Step 1: Draw a diagram representing the situation. Label the tree as point T, the base of the tree as point B, and your location as point A. Draw a line connecting points A and B, and another line from point B extending vertically to point C (representing the height of the tree).
Step 2: Use the given information to identify the known lengths and angles. We know that the distance from you to the base of the tree, AB, is 28 meters. The angle of elevation from your feet to the tree, ∠A, is 26 degrees, and the angle at the base of the tree, ∠B, is 7 degrees.
Step 3: To calculate the height of the tree, we can break down the triangle ABT into two right-angled triangles: triangle ABC and triangle ACT.
Step 4: Find the length of AC. Since triangle ABC is a right-angled triangle and we know one angle (7 degrees) and the adjacent side AB (28 meters), we can use the trigonometric function tangent (tan) to find the opposite side BC. Use the equation:
tan(∠B) = BC/AB
tan(7) = BC/28
BC = 28 * tan(7)
Step 5: Find the length of CT. In triangle ACT, we know one angle (∠A = 26 degrees) and the adjacent side AC (which we just found in the previous step). We can again use the tangent function to find the opposite side CT. Use the equation:
tan(∠A) = CT/AC
tan(26) = CT/AC
CT = AC * tan(26)
Step 6: Add the lengths BC and CT to find the height of the tree, CT + BC.
Now, substitute the values into the equations and calculate the height of the tree.