Question

Given: ΔABC, CM intersects ABBC = 5, AB = 7CA = 4tle="\sqrt2" alt="\sqrt2" align="absmiddle" class="latex-formula">

Find: CM

Answer 1

Based on the calculations, the length of side CM is equal to 4 units.

How to calculate the length of side CM?

First of all, we would determine the measure of angle B by applying the law of cosine as follows:

B² = A² + C² - 2(A)(C)cosB

Given the following data:

A = BC = 5

B = AC = 4√2

C = AB = 7

Substituting the given parameters into the formula, we have;

(4√(2))² = 5² + 7² - 2 × 5 × 7 × cosB

cos(B) = ((4√(2))² - (5² + 7²))/(-2×5×7)

cos(B) = 0.6

B = cos⁻¹(0.6)

B = 53.13°.

Now, we can find side CM by using sine trigonometry:

sin(B) = CM/BC

CM = BC × sin(B)

CM = 5 × sin(53.13°)

CM = 5 × 0.8

CM = 4 units.

Read more on cosine law here: brainly.com/question/11000638

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