Trigonometric Functions and Parallelograms — Test

Question 16 • Integrated Math II CR SUSD (EX)

In which triangle is the value of x equal to tangent inverse of open paren 3 point 1 over 5 point 2 close paren ? (Images may not be drawn to scale.)

Answer

Image with description A right triangle has a right angle at the lower-right vertex and angle x at the top vertex. The bottom horizontal side is labeled 3.1, and the slanted side from the lower-left vertex to the top vertex is labeled 5.2.

Image with description A right triangle has a right angle at the upper-left vertex and angle x at the upper-right vertex. The top horizontal side is labeled 3.1, and the slanted side from the lower-left vertex to the upper-right vertex is labeled 5.2.

Image with description A right triangle has a right angle at the upper-left vertex and angle x at the upper-right vertex. The top horizontal side is labeled 3.1, and the left vertical side is labeled 5.2.

Image with description A right triangle has a right angle at the lower-right vertex and angle x at the lower-left vertex. The bottom horizontal side is labeled 5.2, and the right vertical side is labeled 3.1.

Explanation

Tangent of an angle is opposite side divided by adjacent side (not the hypotenuse). In choice D, relative to angle x, the opposite side is 3.1 and the adjacent side is 5.2, so tan(x) = 3.1/5.2. Therefore x = tan⁻¹(3.1/5.2), matching the triangle in choice D.

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