You can use trigonometry to find the height of a building as shown in Figure P3.

Question

You can use trigonometry to find the height of a building as shown in Figure P3.13. Suppose you measure the angle between the line of sight and the horizontal line connecting the measuring point and the building. You can calculate the height of the building with the following formulas: tan(theta) = h/d h = d tan(theta) Assume that the distance to the building along the ground is 120 m and the angle measured along the line of sight is 30 degree plusminus 3 degree. Find the maximum and minimum heights the building can be.

Explanation / Answer

As we learned when talking about sine, cosine, and tangent, the tangent of an angle in a right triangle is the ratio of the length of the side of the triangle "opposite" the angle to the length of the side "adjacent" to it.

If you think about it, you'll see that the side "opposite" the angle formed between the ground and the line running from me to the top of the tree is the height of the palm tree. And the length of the side "adjacent" this angle is simply the distance from me to the base of the tree. Which means that:

tan( angle ) = height / distance

If we turn this equation around, we can solve for the height of the tree in terms of the tangent of the angle and the distance to the tree:

height = tan( angle ) x distance

Bingo! This equation was my key to finding the height of the tree.

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