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2 years ago

Plslslsllslslslslslslsl helppp

Mathematics

1 answer:

ANEK [815]2 years ago

4 0

Answer:

BE = 39/5 or 7.8

Step-by-step explanation:

As <ABC = <DBE trigonometric function is angle BAC and angle BED

so sin (<ABC) = sin(<DBE) and AC and BC , BD and BE

so AC/AB = DE/BE = 13/BE = 5/3

So now we cross multiply

BE = 13 × 3 over 5

13 × 3 = 39

and over 5 means

39/5 = 7.8

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3 years ago

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4 years ago

In the pulley system shown in this figure, MQ = 30 mm, NP = 10 mm, and QP = 21 mm. Find MN.

ankoles [38]

<h2>Answer:</h2>

$\boxed{\overline{MN}=37.96}$

<h2>Step-by-step explanation:</h2>

For a better understanding of this problem, see the figure below. Our goal is to find $\overline{MN}$ . Since:

$\angle MRS=\angle MQP=90^{\circ} \\ \\ \overline{MQ}=\overline{MR}=30mm$

and $\overline{MN}$ is a common side both for ΔMRN and ΔMQN, then by SAS postulate, these two triangles are congruent and:

$\overline{RN}=\overline{QN}$

By Pythagorean theorem, for triangle NQP:

$\overline{QN}=\sqrt{\overline{NP}^2+\overline{QP}^2} \\ \\ \overline{QN}=\sqrt{10^2+21^2} \\ \\ \overline{QN}=\sqrt{541}$

Applying Pythagorean theorem again, but for triangle MQN:

$\overline{MN}=\sqrt{\overline{MQ}^2+\overline{QN}^2} \\ \\ \overline{MN}=\sqrt{30^2+(\sqrt{541})^2} \\ \\ \boxed{\overline{MN}=37.96}$

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