Question

What is the best approximation of the value of a? 2. 4 cm 2. 7 cm 3. 0 cm 3. 3 cm.

Answer 1

You can use the sine law for the given triangle to find the measure of a.

The value of a is given by

Option D: 3 cm

What is law of sines?

For any triangle ABC, with side lengths |AB| = c units, |BC| = a units, and |AC| = b units, then

$\dfrac{sinA}{a} = \dfrac{sinB}{b} = \dfrac{sinC}{c}$

(If you draw it, you will notice that sin of an angle is sitting over the side length of its opposite side. This is the most important thing that people can mistake most commonly).

Using the above fact to calculate the measure of 'a' for the given context

We have these data

sin A = sin(40 degrees) = 0.643 approx

sin(b) = sin(95) degrees) = 0.996 approx

b = 4.7 cm

Using the first two inequalities, we get

$\dfrac{sinA}{a} = \dfrac{sinB}{b} \\\\\dfrac{0.643}{a} = \dfrac{0.996}{4.7}\\\\a = \dfrac{0.643}{0.212} \approx 3 \: \rm cm$

Thus,

The value of a is given by

Option D: 3 cm

Learn more about sine law here:
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