Question:
Triangle LAY is a right triangle with angle L as it's right angle. Given the measures of angle A=48° and the length of LY= 13cm, which trigonometric ratio can be used to solve for the length of AY?
A. Sine B. Cosine C. Tangent D. Secant
Answer:
Based on the given figure,
Reference Angle = Angle A = 48°
Opposite Side = Length of LY = 13 cm
Hypotenuse Side = Length of AY
Adjacent Side = not given
In order to solve the Length AY (hypotenuse) we need to use a trigonometric ratio that uses both the Hypotenuse and Opposite Side.
Based on the choices, only Sine ratio is possible to solve the length of LY,
[tex]\large {\sf \sin\theta = \frac{opposite}{hypotenuse}}[/tex]
The other choices all uses Adjacent as one of its ratio and since the length of adjacent is not given, we cannot solve the length AY by using these trigonometric ratios.
[tex]\large {\sf \cos\theta = \frac{adjacent}{hypotenuse}}\\\\\large {\sf \tan\theta = \frac{opposite}{adjacent}}\\\\\large {\sf \sec\theta = \frac{hypotenuse}{adjacent}}[/tex]
Hence the correct answer is letter A. Sine
* as always, double check my answers for errors or carelessness.
#No to copy paste solution
#No to plagiarism
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