Math III - 7.1 DHQ (3rd) 12/3

Front

What is the formula to estimate the height of an object using a kite's angle of elevation?

Back

The height can be estimated using the formula: \( h = d \cdot \tan(\theta) \), where \( h \) is the height, \( d \) is the distance from the observer to the base of the object, and \( \theta \) is the angle of elevation.

Front

Define angle of elevation.

Back

The angle of elevation is the angle formed by the horizontal line and the line of sight to an object above the horizontal.

Front

What is the relationship between angles in a right triangle?

Back

In a right triangle, the sum of the angles is always 180 degrees, with one angle being 90 degrees.

Front

How do you find the measure of an angle using trigonometric ratios?

Back

You can find the measure of an angle using the inverse trigonometric functions: \( \theta = \arcsin(\frac{opposite}{hypotenuse}) \), \( \theta = \arccos(\frac{adjacent}{hypotenuse}) \), or \( \theta = \arctan(\frac{opposite}{adjacent}) \).

Front

What is the tangent of an angle in a right triangle?

Back

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side: \( \tan(\theta) = \frac{opposite}{adjacent} \).

Front

If angle A measures 24 degrees, what is the measure of its complement?

Back

The complement of angle A is found by subtracting it from 90 degrees: \( 90 - 24 = 66 \) degrees.

Front

What is the formula for finding the height of a tree using a kite?

Back

The height of the tree can be estimated using the formula: \( h = \frac{d \cdot h_k}{d_k} \), where \( h_k \) is the height of the kite, \( d \) is the distance from the observer to the tree, and \( d_k \) is the distance from the observer to the kite.

Front

How do you solve for x in a right triangle when given two sides?

Back

You can use the Pythagorean theorem: \( a^2 + b^2 = c^2 \) to find the missing side, where \( c \) is the hypotenuse.

Front

What is the sine of an angle in a right triangle?

Back

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse: \( \sin(\theta) = \frac{opposite}{hypotenuse} \).

Front

What is the cosine of an angle in a right triangle?

Back

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse: \( \cos(\theta) = \frac{adjacent}{hypotenuse} \).