A woman 1.7m in height observes the angle of elevation of a tree to be 24°. If she is standing 15m from the tree,determine the height of the tree
8.4m
height above her height:
tan24=d/15
solve for d. Then height of tree is h=d+1.7
From a coastal lookout point P, 100m above sea-level, a soldier sights a boat at an angle of depression of 27 degrees. Calculate the horizontal distance of the boat from the sailor.
To determine the height of the tree, we can use trigonometric ratios involving the angle of elevation. In this case, we can use the tangent ratio.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this scenario, the tree's height is the opposite side, and the distance from the woman to the tree is the adjacent side.
Let's denote the height of the tree as "h".
Using the given information:
Angle of elevation = 24°
Distance from the woman to the tree = 15m
We can set up the following equation using the tangent ratio:
tan(24°) = h / 15
To find the height of the tree, we rearrange the equation to solve for "h":
h = 15 * tan(24°)
Using a calculator, evaluate the right side of the equation:
h ≈ 15 * 0.44504187
h ≈ 6.675628 m
Therefore, the height of the tree is approximately 6.68 meters.