C = 90 degrees, values of sinA, sinB, sinC form geometric sequence. Find value of sinA

[hearts123]

Hi everyone

I have a right triangle ABC, with angle C = 90 degrees.
The values of sinA, sinB, and sinC form a geometric sequence.
What is the value of sinA?

For this question, I'm really not sure where to start. These are all the instructions/information I received in the question. Any help would be very much appreciated!

 

[Dr.Peterson]

Label the sides of the right triangle a, b, and c as usual. What are sin(A) and sin(B)? Keep in mind that sin(90°) = 1.

Then write what it means for sin(A), sin(B), and sin(C) to be a geometric sequence. This gives you an equation, which together with the Pythagorean Theorem can be solved to find the ratios. (You may find it helpful to assume c=1, since all that matters are the ratios.)

If you need more help, be sure to show your work so we can see what hint you need next.