Here are some general tips on how to identify standout players:
\[c^2 = a^2 + b^2 - 2ab \cos(C)\]
\[6.3^2 = 4.3^2 + 5.1^2 - 2 \cdot 4.3 \cdot 5.1 \cos(C)\]
\[39.69 = 18.49 + 26.01 - 43.53 \cos(C)\]
\[39.69 = 44.50 - 43.53 \cos(C)\]
Rearrange to isolate \(\cos(C)\):
Now, find the angle \(C\) by taking the arccosine:
\[C \approx \cos^{-1}(0.1106)\]
Therefore, the smallest angle in the triangle is approximately \(83.79^\circ\).
1. Samia is 7 years older than Amina: \(s = a + 7\)
2. The fraction of Samia's age is equal to half of Amina's age: \(\frac{ 1}{4}s = \frac{1}{2}a\)
Now let's replace the expression for Samia's age in the first equation with the second equation:
\[\frac { 1} {4}(a + 7) = \frac{1}{2}a\]
Multiply both sides by 4 to subtract the fraction:
Now that we know Amina's age (\(a = 7\)), we can find Samia's age using the first equation:
There are several ways to prove the equation x² + y² = (x + y)(x – y). Here are two common methods: Method 1: Expanding the Binomial Pro...