Question

iia)
in △ abc,
a= 17, b = 21, c = 30
find m ∠ b

Explanation:

Step1: Recall the Law of Cosines

To find the measure of angle \( B \) in triangle \( ABC \) with sides \( a = 17 \), \( b = 21 \), and \( c = 30 \), we use the Law of Cosines. The formula for the Law of Cosines when finding angle \( B \) is:

$$ \cos B=\frac{a^{2}+c^{2}-b^{2}}{2ac} $$

Step2: Substitute the given values

Substitute \( a = 17 \), \( b = 21 \), and \( c = 30 \) into the formula:
First, calculate \( a^{2}=17^{2} = 289 \), \( b^{2}=21^{2}=441 \), and \( c^{2}=30^{2} = 900 \).
Then, \( a^{2}+c^{2}-b^{2}=289 + 900-441=748 \).
And \( 2ac=2\times17\times30 = 1020 \).
So, \( \cos B=\frac{748}{1020}\approx0.7333 \).

Step3: Find the angle

To find \( B \), we take the inverse cosine (arccos) of \( 0.7333 \):
\( B=\arccos(0.7333)\approx42.83^{\circ} \) (using a calculator to find the arccos value).

Answer:

The measure of angle \( B \) is approximately \( 42.83^{\circ} \) (or depending on the calculator's precision, it can be rounded appropriately, for example, \( 43^{\circ} \) if rounding to the nearest degree).