- Advertisement -

"Society & Culture & Entertainment" MOST POPULAR

- Advertisement -

# How to Find Unknown Angles

104 17
• 1). Know and understand what numbers you have, what they mean and what the formulas are for solving the angles. Let's say that you don't know any of the interior angles; all you know are the exterior sides: Side a = 3, Side b = 4 and Side c = 6.

• 2). Understand that you always need to find the largest angle first (because only one angle can be greater than 90 degrees). In this example, Side c is the largest. Use the cosine rule to find angle C: c^2 = b^2 + a^2 - 2ba(cosC)

Add 2ba(cosC) from both sides to pull it to the left of the equation and subtract c^2 from both sides to pull it to the right. Also, reverse b^2 with a^2 so that a^2 is in the front.

2ba(cosC) = a^2 + b^2 - c^2

Now divide 2ba from both sides.

cosC = a^2 + b^2 - c^2 / 2ab

Plug in your numbers and solve.

cosC = 3^2 + 4^2 - 6^2 / 2 x 3 x 4
= (3 x 3) + (4 x 4) - (6 x 6) / 2 x 3 x 4
= 9 + 16 - 36 / 24
= -11 / 24

cosC = - 0.46

Now find the inverse cos of -0.46 by using your calculator.

C = cos^-1 (-0.46)

Angle C = 117.279 degrees

• 3). Find angle A using the sides of the triangle and angle C. To find angle A, you will use the sine rule: a / sin A = c / sinC

Multiply a from both sides to solve for sinA. Also, reverse c with sinC.

sinA = a sinC / c

Plug in your numbers to solve.

sin A = 3 x sin 117.279 / 6

Input 117.279 then "sin" on your calculator.

sin A = 3 x .889 / 6
sin A = 2.667 / 6
sin A = 0.445

Determine the inverse sin of 0.445 using your calculator.

A = sin^-1 (0.445)

Angle A = 26.423 degrees

• 4). Find angle B by using the Sum of Internal Angles rule. All the internal angles have to add up to 180. The actual equation is: A + B + C = 180.

Subtract (A + C) from both sides to solve for B.

B = 180 - (A + C)
B = 180 - (26.423 + 117.279)
B = 180 - 143.702
B = 36.298

Angle B = 36.298 degrees

Subscribe to our newsletter
Sign up here to get the latest news, updates and special offers delivered directly to your inbox.
You can unsubscribe at any time
Stay With Us