Question

What is the missing value of X if there is a triangle with the sides 6x, 3x+12, and x + 25 and the angles of 70 degrees and 40 degrees (the third angle is not there)

Answer 1

We can use the law of sines, which relates the angles and sides of a triangle.
The formula is:
$\frac{sinA}{a}= \frac{sinB}{b}= \frac{sinC}{c}$,
where A, B, and C are angles and a, b, c are side lengths.

Let's find the missing angle. The interior angles of a triangle add up to 180 degrees, so the missing angle is 180-70-40 = 70 degrees.

Let's make a proportion and use the two 70 degrees angles and their opposite lengths. Since both sides have the same numerator of 70 degrees, we can equate the denominators together.
$\frac{sin70}{x+25}= \frac{sin70}{6x} \\ \\ x + 25 = 6x \\ 25 = 5x \\ x = 5$