If you're looking for side lengths or angle measurements of a triangle, you can use the law of sines or cosines to find them.The law of sines is asin.There is a law of cosines.The side lengths of the triangle are in each formula.The angle opposite each side has a variable.These two laws can be used to solve missing information if you know enough about your triangle.
Step 1: Determine what you know.
To find a missing side, you need to know at least two angles of the triangle and one side length.You know that the side opposite the 39 degree angle is 4 cm long if you have a triangle with two angles measuring 39 and 52 degrees.The law of sines can be used to find missing side lengths.
Step 2: You should identify sides and opposite angles.
Side lengths are labeled as displaystyle a, b, and c.The capital letter of that side's variable shows the angle opposite each side.The angle between side A and side B is A, and the side C is B.You have a triangle with a display style of a=4 cm.Is it displaystyle b?The style of the B is 52 degrees.Can you tell me the style of the display?Is it C?C is a style of display.
Step 3: Find the angle that's missing.
180 degrees is the sum of the angles in a triangle.You can find the third angle by subtracting the two angles from 180.For example, since A is 39 degrees and B is 52 degrees.
Step 4: The law of sines has a formula.
The formula is asin A, B, and C.The formula shows that the ratio of one side of the triangle to the opposite angle is the same for all sides.
Step 5: Plug all the values into the formula.
Substitute side lengths and angles for the capital variables.The opposite sides and angles should have the same letter.For example, 4sin39 is a display style.
Step 6: You can use a calculator to find the angles.
A trigonometry table can also be used.The ratios have sines in them.For example, sin39 is displayed with a displaystyle of 0.6293.Your ratios will look like this: 40.6293b0.788c0.9998displaystyle.
Step 7: The complete ratio needs to be simplified.
There is a complete ratio with an angle and side.Divide the numerator by the denominator to simplify it.40.6293 is a example.
Step 8: The incomplete ratios should be equal to the complete ratio.
To solve for a missing variable, take the complete ratio and divide it by the incomplete ratio.6.3562 is a displaystyle that says "frac b0.788"
Step 9: Understand what you know.
To find a missing angle, you need to know at least two side lengths and one angle.You could have a triangle with one side that is 10 cm long.One side is 8 cm long and the other is 50 degrees away.The side is 10 cm long.
Step 10: You should identify sides and opposite angles.
Side lengths are labeled as displaystyle a, b, and c.The capital letter of that side's variable shows the angle opposite each side.The angle between side A and side B is A, and the side C is B.In your triangle, for example, a=8 cm, A50 degrees, and B10 cm.B is a style of display.Can you tell me the style of the display?Is it C?C is a style of display.You are looking for angle B since you want to find the angle opposite the 10 cm side.
Step 11: The formula for the law of sines needs to be set up.
The formula is asin A, B, and C.The formula shows that the ratio of one side of the triangle to the opposite angle is the same for all sides.
Step 12: Plug all the values into the formula.
If you substitute the values correctly, the side lengths of the formula will be in the numerators.8sin 50 is the displaystyle for example.
Step 13: The equation should be used to find the missing angle.
The complete ratio should be equal to the ratio with the angle you are solving for.Take the inverse of each ratio so that the side length is in the numerator.Since you know side A and angle A, and are solving for angle B, you would set up the ratio 8sin.You have sin508, sinB10displaystyle, and 508, if you take the reciprocates.
Step 14: The angle is known by the sine of it.
You can use a calculator to do this.The decimal should be plugged into the equation.The display style is sin50=0.766.The equation should now look like this.
Step 15: The equation can be simplified if the missing sine is isolated.
To simplify the equation, take each side of it and divide it by the unknown angle's denominator.For example:sin 508
Step 16: The inverse sine can be found.
The inverse sine can be seen on a calculator.You can measure the missing angle with the inverse sine.The inverse sine of 0.9575 is 73.2358.The angle is 73.24 degrees.
Step 17: Determine what you know.
To find a missing side length, you need to know the length of the other two sides and the angle between them.The angle between the sides of the triangle is 85 degrees.You have to find the length of the missing side.
Step 18: Pick out sides and opposite angles.
Side lengths are labeled as displaystyle a, b, and c.The capital letter of that side's variable shows the angle opposite each side.The angle between side A and side B is A, and the side C is B.You have a triangle with a displaystyle of a=5 cm.Is it style A?B is the style of display which is 9 cm.B is a style of display.Can you tell me the style of the display?Since you want to find the side opposite the 85 degree angle, you are looking for side c.
Step 19: The law of cosines has a formula.
The formula is c2.The side length is missing in this formula.
Step 20: The known values should be put into the formula.
Substitute the correct values for the wrong variables.The side you are looking for should be displaystyle c, and the angle you know is C.There is a displaystyle called c2=52+ 922(5)(9)cos 85.
Step 21: You can use a calculator to find the angle.
Plug this value into the equation.For example, the style of cos is cos.Your equation should now look like this.
Step 22: Square the side lengths.
To square a number is to multiply it by itself.Add the numbers together by squaring them.For example:c2 is 25+ 817.844.
Step 23: Find the difference.
The value of c2displaystyle will be given by this.You can find displaystyle c by taking the square root of both sides of the equation.For example:c2 is 1067.844 and it's displaystyle is 98.156.
Step 24: Determine what you know.
You need to know the length of all three sides of the triangle to find the missing angle.You could have a triangle with the sides measuring between 14 and 17 cm.The angle has to be opposite the 20 cm side.
Step 25: Pick out sides and opposite angles.
Side lengths are labeled as displaystyle a, b, and c.The capital letter of that side's variable shows the angle opposite each side.The angle between side A and side B is A, and the side C is B.You have a triangle with a displaystyle of 14 cm.Is it style A?The display style is 17 cm.Is it displaystyle B?C=20 cm is the display style.C is a style of display.The side opposite the 20 cm side is what you are looking for.
Step 26: The law of cosines has a formula.
The formula is c2.The angle you are trying to find is Cdisplaystyle C.
Step 27: Plug all the values into the formula.
Substitute the correct values for the wrong variables.The angle you are looking for should be displaystyle C.C should be the side opposite of the angle you are trying to solve.For example, 202 is a displaystyle of 202
Step 28: Use the order of operations to simplify the expression.
The side lengths have squares.The appropriate multiplications should be made.Then add.For example: 142+1722(14)(17)cosCdisplaystyle 202.
Step 29: The cosine should be isolated.
If you want to do this, you have to subtract the squares of sides from the equation.Divide each side by the coefficients.For example, if you want a displaystyle of 400, you can use 476.
Step 30: The inverse cosine can be found.
The key is on a calculator.You can get the measurement of the missing angle with the inverse cosine.The inverse cosine of 0.1786 is 79.7134.The angle is about 78.51 degrees.