How do I find a side of a triangle using pythagorian therum with an angle?

Question

For example lets say the question is this:

A equals 6
B equals 9
And the angle of b and c is 30 how do I solve this problem? It confuses me I am not sure what equation to use.

Answer 1

you can never solve the other side by pythagorean theorem because the example u've given is not right triangle but you can make use of the cosine law which is a^2=b^2+c^2-2bccosA where a,b,c are the sides and A is the angle...u can also use the sine law!!!

Answer 2

If Angle BC=30, then either B or C is the hypotenuse. Assuming that C is the hypotenuse, then C^2=6^2+9^2=117, C=10.82
Assuming that B is the hypotenuse, then 9^2=6^2+C^2, C^2=45, C=6.71

Answer 3

Pythagorean method;

Create a right triangle, hypotenuse B (longer side). Angle 1 is 30 degrees. Sides are segments C and D, where A is part of segment C.

Based on sin(30), segment D is 4.5 (half of B). Segment C can then be found.

9^2 = (4.5^2) + C^2
81 = 20.25 + c^2
c = (60.75^.5) or about 7.8

Within the first triangle, you create a second triangle (it's angles are not immediately relevant, other than the 90), using segment D as one side, part of segment C as the other side, and your unknown 3rd side as the hypotenuse. The part of segment C being used is the part not on A.

Cseg = 7.8 - 6 = 1.8

Unknown (3rd) side of original triangle
(4.5^2) + (1.8^2) = x^2
20.25 + 3.24 = x^2
x = 4.84

Trig method;

Same basic method, create two right triangles, one within the other. Instead of using Pythagorean theorem, use the trig as ratios to determine the missing values.

Remember it as follows;

sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent

Answer 4

You can't use the Pythagoras rule, because you don't know that there is a right angle in the triangle. Use the Sine Rule:

A / Sin(a) = B / Sin(b) = C / Sin(c)

Here, a, b and c are the angles opposite sides A, B and C.

Answer 5

The hypotenuse will never make right angle with any side in your case c is the hypotenuse.a^2 + b^2 = c^2

Answer 6

cos(30) = A/C

Therefore, C = A/cos(30)

=6/(sqrt(3)/2)

= 4*sqrt(3)

Answer 7

drop a perpendicular to the base

Answer 8

arghhh...... my brain hurts