I have right triangles I need to solve. Can you see if I am doing them correctly or screwed up..1) Rt < is in left corner C: Opposite is 60 deg< A, last angle is at top- 30 deg <. line segment of AB is 10. Hypo is f. I got 10 0r 12.5 for answer. 2) Triangle is ABC with rt angle on left. AB is 10. hyp is 20, altitude is H. I got 3 sq rt of 10 for answer. 3) rt triangle with left side 90 deg <. Hypo is b, altitude is 4, base AC is a. I got a=6, b=4. Did I bomb?

Question

I have right triangles I need to solve. Can you see if I am doing them correctly or screwed up..1) Rt < is in left corner C: Opposite is 60 deg< A, last angle is at top- 30 deg <. line segment of AB is 10. Hypo is f. I got 10 0r 12.5 for answer. 2) Triangle is ABC with rt angle on left. AB is 10. hyp is 20, altitude is H. I got 3 sq rt of 10 for answer. 3) rt triangle with left side 90 deg <. Hypo is b, altitude is 4, base AC is a. I got a=6, b=4. Did I bomb?

Answer 1

1)

in a 30-60-90 triangle, the sides are in the proportion 1:√3:2

2)
h^2+10^2 = 20^2

3)
a^2+4^2 = b^2
unless you know one of the other angles, there are lots of a and b which will work.