Find sec0, sin0, tan0, where 0 is shown in the figure.right triangle. Hypotenuse=9, base=4

Question

It is a right trangle. Base is 4. Hypotenuse is 9. The point of the angle says 0

Answer 1

Edyson,

 

If I understand you correctly, what you have is an angle θ in a right triangle with hypotenuse 9 and base 4. Without knowing where the angle is in this triangle, I can not definitely answer your question, SO I will assume that the angle is formed by the base and the hypotenuse.

 

Using the Pythagorean Theorem, the third side (leg opposite the angle θ), has length √(9²-4²) = √65.

 

You can then find the sec, sin, and tan of θ using the standard trig ratios in this triangle:

 

sin θ = opposite/hypotenuse = (√65)/9

tan θ = opposite/adjacent = (√65)/4

sec θ = adjacent/hypotenuse = 4/9

 

Let me know if you have any questions on my explanation.