When we want to solve a triangle, this means that we want to find all/some of the unknown lengths and angles of the triangle.
A triangle has side lengths and and . What is the length of the third side,
By the cosine rule, we have . Substituting all the relevant information, we have . Since represents a side length of a triangle, only, so .
If the area of a triangle is given to be 20 unit squared with two of its side lengths being 7 and 8, what is the sine of the angle in between these two side lengths?
Using the area formula, Solving for the sine of the angle gives
The area of an acute triangle is 10, and two side lengths of the triangle are 6 and 7. What is the cosine of the angle in between these two sides?
Let the angle between the two sides be Then the area of the triangle is which gives
By applying the Pythagorean identity, so
Note that we are only taking the positive root because the cosine of an acute angle is strictly positive.
The numerical value of the area of a triangle is given to be . What is the relationship between the product of the sides of the triangle to the product of sines of the angles of the triangle?
Let denote the area of the triangle, then . Then,
So the relationship in question is simply
A semi-circle is inscribed within an equilateral triangle such that the diameter of the semi-circle is centered on one side of the triangle and the arc is tangent to the other two sides.
If each side of the triangle is of length 4 cm, then what is the diameter of the semi-circle (in cm)?
Give your answer to 3 decimal places.