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2 years ago

What is the length of the altitude of the equilateral triangle below?

Mathematics

1 answer:

ElenaW [278]2 years ago

5 0

Answer:

Step-by-step explanation:

the height a creates with half of the baseline (5) and a leg (10) a right-angled triangle, and we can use Pythagoras to calculate a.

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle, so in our case the 10 side).

10² = a² + 5²

100 = a² + 25

75 = a²

a = sqrt(75) = sqrt(3×25) = 5×sqrt(3)

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Given PQ = 24

Verdich [7]

The shape PQRS is a parallelogram

The measure of angle QRS is 70 degrees
The measure of angle PQS is 53 degrees
The measure of angle RPS is 35 degrees
The measure of angle PSQ is 53 degrees

The given parameters are:

$\mathbf{\angle PQR = 106}$

$\mathbf{\angle QSR = 49}$

$\mathbf{\angle PRS = 35}$

(a) Find QRS

This is calculated as:

$\mathbf{\angle QRS = 2 \times \angle PRS }$

So, we have:

$\mathbf{\angle QRS = 2 \times 35}$

$\mathbf{\angle QRS = 70}$

Hence, the measure of angle QRS is 70 degrees

(b) Find PQS

This is calculated as:

$\mathbf{\angle PQS = \frac 12 \times \angle PQR }$

So, we have:

$\mathbf{\angle PQS = \frac 12 \times 106}$

$\mathbf{\angle PQS = 53}$

Hence, the measure of angle PQS is 53 degrees

(c) Find RPS

This is calculated as:

$\mathbf{\angle RPS = \angle PRQ }$

Where:

$\mathbf{\angle PRQ = \angle PRS = 35}$

So, we have:

$\mathbf{\angle RPS = 35}$

Hence, the measure of angle RPS is 35 degrees

(d) Find PSQ

This is calculated as:

$\mathbf{\angle PSQ =\frac 12 \times \angle PQR }$

Where:

$\mathbf{\angle PSQ =\frac 12 \times \angle 106}$

So, we have:

$\mathbf{\angle PSQ =53}$

Hence, the measure of angle PSQ is 53 degrees

Read more about angles in a parallelogram at:

brainly.com/question/12186483

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3 years ago

Maar of the towns que

aalyn [17]

Answer:

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Step-by-step explanation:

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A company produces jam in three flavors: strawberry, raspberry, and grape. Each flavor is sold in 200-gram and 400-gram jars. Th

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From the table, there were 1,150 jars of 200gm and 900 jars of 400gm raspberry jam sold, thus, the revenue from the sales of raspberry jam is given by 3(1,150) + 5(900) = 3,450 + 4,500 = $7,950.

From the table, there were 950 jars of 200 gm and 1050 jars of 400 gm grape jam sold, thus, the revenue from the sales of grape jars is given by 3(950) + 5(1,050) = 2,850 + 5,250 = $8,100.

Therefore, among the three flavors, raspberry jam earned the least revenue for the company.

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