This is trigonometry:
A tree's height is unknown so we have to solve for the height of the tree. The tree casts a 11m shadow. And the angle of the triangle is 36 degrees.
Sorry 34 degrees!!!!
Assuming you made a sketch, and the 34° angle is at the end of the shadow, then
h/11 = tan34
h = 11tan34
= ...
To solve for the height of the tree using trigonometry, we can use the tangent function. The tangent function relates the ratio of the opposite side of a right triangle to the adjacent side.
In this case, the height of the tree is the opposite side, and the length of the shadow is the adjacent side. The angle between the ground and the direction of the sun's rays is 36 degrees.
Here's how you can calculate the height of the tree step-by-step:
Step 1: Set up the equation.
Using the tangent function, we have:
tan(angle) = opposite / adjacent
Plugging in the values we know:
tan(36°) = height of tree / length of shadow
Step 2: Solve for the height of the tree.
To isolate the height of the tree, we multiply both sides of the equation by the length of the shadow:
length of shadow * tan(36°) = height of tree
Now we can substitute the values given:
11m * tan(36°) = height of tree
Step 3: Calculate the height of the tree.
To find the approximate value of the tangent of 36 degrees, use a calculator. Assuming a decimal approximation of 0.7265:
11m * 0.7265 = height of tree
height of tree ≈ 7.99m
Therefore, the height of the tree is approximately 7.99 meters.