A 12-meter tall building casts a 16-meter long shadow on level ground. Find the angle, in degrees, that the sun makes with the ground (use the appropriate inverse trigonometric function).

Given a building with a height of 12 meters and a shadow length of 16 meters.

Identify the Trigonometric Relationship:
We’ll use the tangent function (tan) because it relates the opposite side (height of the building) to the adjacent side (length of the shadow) in a right triangle.

Write down the equation for tangent:

\$tan(θ) = "opposite"/"adjacent"\$

Substitute the height of the building and the length of the shadow into the equation:

\$tan(θ) = 12/16\$

\$tan(θ) = 3/4\$

Use the Inverse Tangent Function: To find the angle θ, use the arctangent function (inverse tangent):

\$θ = arctan( 3/4)\$

\$θ = 36.87°\$

The angle that the sun makes with the ground is approximately 36.87°.

This value is close to 30 degrees. It might have been calculated by approximating the ratio of the opposite side to the adjacent side in the right triangle formed by the building and its shadow

30.96 degrees

This value is a common angle in trigonometry, representing a right triangle where both legs are equal. However, it’s not the correct answer for this specific scenario unless the height of the building and the length of its shadow were equal

45 degrees

This is the correct answer. It’s obtained by accurately calculating the inverse tangent of the ratio of the building’s height to the length of its shadow

36.87 degrees

This value is another common angle in trigonometry, representing an equilateral triangle. However, it’s not the correct answer for this scenario as it doesn’t correspond to the given dimensions of the building and its shadow

60 degrees

Option

C

Can you summarize what you’ve understood in the above steps?