SOLUTION: Trying to figure one side of a 90 degree triangle. vertical leg a=0.75", horizontal leg b=? "tbd, angle from b to a is 90 dree, at the top of vertical leg a is a 30 degree angle.

Question 959272: Trying to figure one side of a 90 degree triangle. vertical leg a=0.75", horizontal leg b=? "tbd, angle from b to a is 90 dree, at the top of vertical leg a is a 30 degree angle. What is the horizontal distance from the vertical leg a to the point of the triangle?
Found 2 solutions by macston, addingup:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
x=leg b
tan(30)=x/0.75"
If I read your question correctly, leg a is adjacent the 30 degree angle
and leg b is opposite: opposite/adjacent=tangent
.
0.75"*tan(30)=x
0.433"=x ANSWER: The length of leg b=0.433 in

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
This is a very special right triangle. Right angles have the characteristic of having one 90 degree angle.
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When the problem tell you that another angle is either a 30 degree or 60 degree angle, you immediately know that you're dealing with a 30-60-90 because the angles of EVERY triangle sum 180. Look at my picture, the triangle on the right shows you the ratio that applies to every one of these special 30-60-90 triangles:
1, 2, square root of 3.
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Your problem gives you one measurement: 0.75 This is for the long leg, the ratio of which is 1.732 Therefore, the horizontal distance from the vertical leg "a" to the point of the triangle is:

The hypotenuse is twice that:

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You can also use trigonometry. SOHCAHTOA helps you with which one to use in each case. In this case, we know the adjacent side (side a) and want to find out what the opposite side is (side b), therefore we use TOA:

flip the equation
Use your calculator to find the tan for 30:
Now multiply both sides by 0.75:
As you see, we used a different method but got the same answer as above.
P.S.: I hope you find the illustration I made you helps you.

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