#2.16 Flashcardizz -- Indirect Measurement

Front

What is indirect measurement?

Back

Indirect measurement is a technique used to measure an object or distance that cannot be directly measured, often using similar triangles or proportional relationships.

Front

How do you find the height of an object using indirect measurement?

Back

To find the height of an object using indirect measurement, you can use the properties of similar triangles or the shadow method, where the ratio of the height to the shadow length is equal to the ratio of the height of another object to its shadow length.

Front

What is the formula for similar triangles?

Back

If two triangles are similar, the ratios of their corresponding sides are equal. This can be expressed as: a/b = c/d, where a and b are sides of one triangle, and c and d are sides of the other.

Front

If a tree casts a shadow of 10 feet and a 6-foot person casts a shadow of 4 feet, how tall is the tree?

Back

Using the ratio of shadows: (Height of tree)/(10) = (6)/(4). Solving gives the height of the tree as 15 feet.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

How can you use a right triangle to measure the height of a building?

Back

You can measure the distance from the building and the angle of elevation to the top of the building. Using trigonometric ratios, you can calculate the height.

Front

What is the tangent function in trigonometry?

Back

The tangent function relates the angle of a right triangle to the ratio of the opposite side to the adjacent side: tan(θ) = opposite/adjacent.

Front

If you know the distance from a point to a tree and the angle of elevation to the top of the tree, how can you find the height of the tree?

Back

You can use the tangent function: height = distance * tan(angle of elevation).

Front

What is the purpose of using indirect measurement in real life?

Back

Indirect measurement is used in various fields such as construction, surveying, and navigation to measure distances and heights that are difficult to access directly.

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where their ratio remains constant.