SaiBook.us SAT-2

Lesson Example Discussion Quiz: Class Homework

Example

Title: Angle measurement (degrees, radians)

Grade: 1400-a Lesson: S3-L6

Explanation: The best way to understand SAT-2 is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

Sarah is standing at point A and looking at the top of a tower. The angle of elevation from Sarah’s eyes to the top of the tower is 30 degrees. If Sarah is standing 50 meters away from the base of the tower, how tall is the tower? Express your answer in radians.

Step 1a

The given angle of elevation = 30, Distance from the base of the tower to Sarah = 50 meters.

Let h be the height of the tower.

Using the tangent function, we have:

\$"tan"(30) = "h"/50\$

\$"h" = "tan"(30) times 50\$

h = 28.86 m

Explanation: Use the tangent function to determine tower height based on the provided angle of elevation and distance.

Step 1b

Convert the angles from degrees to radians: \$"Radians" = "Degree" times (pi)/180\$

Plug the value in the formula: \$"Radians" = 30 times (pi)/180\$

\$"Radians" = \cancel(30) times (pi)/\cancel(180)^6\$

\$"Radians" = (pi)/6\$

Therefore, the height of the tower is approximately 28.86 meters, and the angle in radians is \$π/6\$.

Explanation: Calculate radians from degrees using the conversion formula to determine the angle in radians.