Trigonometry help: Values of right triangles

[jenyrice]

Can some please help me fihure this out.

#1 I have a right triangle with sides x and y which I am to find the values of. Obviously, one of the angles is 90 degrees and the other is 30 degrees 5', and the hypotenuse is equal to 1. It says find the value of x and y using the appropriate trig functions. How do I do this? Help, please.

#2 I have a right triangle, side a = 3, side b = 5 and the hypotenuse = 4.
Angle AB is 90 degrees. It says find the value of the angle BC in degrees. Use the appropriate trig function. How do I do this?

I would greatly appreciate anyone's help.
Thanks.

 

[stapel]

1) You have a right triangle, with legs x (as the base) and y (as the height), and hypotenuse h, where h has length 1. One of the angles (I'll call it "ß", or "beta") is 30° (or is it 30°5'?). I will guess that this is the angle formed by x and h.

To find the lengths of x and y, note that sin(ß) = y/h = y/1 = y, and cos(ß) = x/h = x/1 = x. So just plug into your calculator.

2) You have a right triangle with all sides labelled. (I've drawn the triangle with point A on the left-hand end of the base b, and point C on the right-hand end of the base. Then B is the upper corner point, and ACB is the right angle.)

Note that sin(BAC) = a/h. Then use the inverse trig function on your calculator.

Eliz.

 

[Denis]

#2 I have a right triangle, side a = 3, side b = 5 and the hypotenuse = 4.
Angle AB is 90 degrees. It says find the value of the angle BC in degrees. Use the appropriate trig function. How do I do this?

Please be careful, jr; hypotenuse CANNOT equal 4:
hypotenuse is always the LONGEST side, and ALWAYS opposite the 90 angle.

A

b                 c

C               a                  B

It is standard to "label" a right triangle like above;
hypotenuse is AB and represented by c (it's opposite C);
AC is a side and represented by b (it's opposite B)
BC is a side and represented by a (it's opposite A)

 

[stapel]

Please be careful, jr; hypotenuse CANNOT equal 4

Geez! I didn't even notice the actual numbers. :shock: :roll:

The methodology I gave is fine, but the particular numbers will have to be adjusted to fit the triangle properly.

Thank you for pointing the correction, Denis!

Eliz.