lets say you have a tree or a flagpole. Describe how you would measure this object using right angled triganometry
stick a stick vertically in the ground.
measure the height and shadow of the stick.
measure the shadow of the tree, and use the same ratio to calculate its height.
extra credit: why does this work?
I think i have to use soh cah toa instead of similar triangles
unless you can measure the angle, you have to use similar triangles. If you can measure the angle sighting from the tip of the stick's shadow to the top of the stick, then
tanθ = opposite/adjacent
The same angle is made from the pole's shadow to the top of the pole.
So, if the shadow is length s, and the pole is height p, then
p/s = tanθ
To measure the height of a tall object such as a tree or a flagpole using right-angled trigonometry, you can use a method called "shadow method." Here's how you can do it:
1. Find a distance from the object. Stand at a distance from the object where you can clearly see its entire height. Ensure that this distance is not too close; otherwise, it may be challenging to measure the height accurately.
2. Place a stick vertically on the ground. Find a spot where the stick's shadow is clearly visible and ensure that it is perfectly vertical.
3. Measure the length of the shadow. Using a ruler or measuring tape, measure the length of the shadow cast by the stick. Note down the measurement in any suitable unit of length (e.g., centimeters or inches).
4. Measure the distance from the shadow to the object. Measure the distance from the shadow of the base of the object to the stick. Again, use a ruler or measuring tape, and note down the measurement.
5. Determine the angle of elevation. Using a protractor, measure the angle between the ground and your line of sight to the top of the object. Ensure that the protractor is aligned correctly with the ground and your line of sight. Note down the measurement as the angle of elevation.
6. Apply trigonometry to calculate the height. Now that you have the shadow length, the distance from the shadow to the object, and the angle of elevation, you can use trigonometry to determine the height. The following trigonometric formula can be used:
height = shadow length * tan(angle of elevation)
Multiply the length of the shadow by the tangent of the angle of elevation to obtain the height of the object.
Remember to use the same units of measurement consistently throughout the calculations to ensure accuracy.