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Elenna [48]
3 years ago
9

What is the value of b?

Mathematics
1 answer:
tresset_1 [31]3 years ago
8 0

Answer:

17

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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Answer:

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Step-by-step explanation:

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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 \displaystyle BC = 2\;MC for M is the midpoint of segment BC.

\rm \displaystyle PB = \frac{4}{3}BC = \frac{8}{3}MC.

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

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

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