Question

Given triangle ABC, which equation could be used to find the measure of ∠C? (1 point) right triangle ABC with AB measuring 6, AC measuring 3, and BC measuring 3 square root of 5 tan m∠C = one half sin m∠C = square root of 5 over 5 sin m∠C= square root of 5 over 2 tan m∠C = 2

Answer 1

The trigonometric function gives the ratio of different sides of a right-angle triangle. The correct option is D, Tan(∠C) = 2.

What are Trigonometric functions?

The trigonometric function gives the ratio of different sides of a right-angle triangle.

$\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}$

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

The given triangle can be made as shown below. Therefore, the measure of ∠C can be written as,

$\rm Sin \angle C= \dfrac{AB}{BC} = \dfrac{6}{3\sqrt5} = \dfrac{2}{\sqrt5}\\\\\\Cos \angle C=\dfrac{AC}{BC}=\dfrac{3}{3\sqrt5}=\dfrac{1}{\sqrt5}\\\\\\Tan \angle C=\dfrac{AB}{AC} = \dfrac{6}{3} = 2$

Hence, the correct option is D, Tan(∠C) = 2.

Learn more about Trigonometric functions:

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