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4 years ago

What is the value of b?

Mathematics

1 answer:

tresset_1 [31]4 years ago

8 0

Answer:

Step-by-step explanation:

Using the law of cosines in ΔABC

b² = a² + c² - (2ac cosB) ← substitute in values

= 25² + 28² - (2 × 25 × 28 × cos36.9°)

= 625 + 784 - 1400 cos36.9°

= 1409 - 1400 cos36.9° ( Take the square root of both sides )

b = $\sqrt{1409-1400cos36.9}$ ≈ 17 ( nearest whole number )

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$\implies \rm 90^{\circ} - \angle B\hat{M}P = \angle C\hat{M}Q$ .

Also,

$\rm \angle B\hat{P}M = 90^{\circ} - \angle B\hat{M}P$ in right triangle PBM.

Thus $\rm \angle{P\hat{B}M} = \angle C\hat{M}Q$ .

Additionally $\rm \angle \hat{B} = 90^{\circ} = \angle \hat{C}$ .

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$\rm \triangle PBM \sim \triangle MCQ$ implies that

$\displaystyle \rm PM:MQ = PB:MC = 1:\frac{8}{3} = 8:3$ .

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