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love history [14]

2 years ago

7

In right triangle PQR, tanP =sqrt 3/2. Find the length of the hypotenuse of triangle PQR.

1 answer:

Aleksandr [31]2 years ago

8 0

$\sqrt{ \sqrt{3}^2+2^2} = \sqrt{3+4} = \sqrt{7}$

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in the figure below trianglePQM and triangleQRP are right triangles. the measure of lineQM is 6 and the measure of lineQP is 8.

Kipish [7]

Answer:

Option 4 is correct. The length of PR is 6.4 units.

Step-by-step explanation:

From the given figure it is noticed that the triangle PQR and triangle MQR.

Let the length of PR be x.

Pythagoras formula

$hypotenuse^2=base^2+perpendicular^2$

Use pythagoras formula for triangle PQM.

$PM^2=QM^2+PQ^2$

$PM^2=(6)^2+(8)^2$

$PM^2=36+64$

$PM^2=100$

$PM=10$

The value of PM is 10. The length of PR is x, so the length of MR is (10-x).

Use pythagoras formula for triangle PQR.

$PQ^2=QR^2+PR^2$

$(8)^2=QR^2+x^2$

$64-x^2=QR^2$ .....(1)

Use pythagoras formula for triangle MQR.

$MQ^2=QR^2+MR^2$

$(6)^2=QR^2+(10-x)^2$

$36=QR^2+x^2-20x+100$

$36-x^2+20x-100=QR^2$ .... (2)

From equation (1) and (2) we get

$36-x^2+20x-100=64-x^2$

$20x-64=64$

$20x=128$

$x=6.4$

Therefore length of PR is 6.4 units and option 4 is correct.

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2 years ago

A red light flashes every 14 minutes. A blue light flashes every 24 minutes. when will the two lights flash together again if th

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3 years ago

The simplified answer of 6/35

Rzqust [24]

The simplified answer of 6/35 is 6/35. It is in simplest form.

7 0

2 years ago

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3 0

3 years ago

Two mechanics worked on the car the first mechanic work for five hours in a sec mechanic work for 15 hours together the tires a

FrozenT [24]

Answer:

Mechanic 1: $55 per hour

Mechanic 2: $105 per hour

Step-by-step explanation:

Given

Represent the rate of the first mechanic with x and the second with y.

So, we have:

$x + y = 160$

The total earnings is: $1850, so we have:

$5x + 15y = 1850$

Required

Determine the rate of each

The equations are:

$x + y = 160$ --- (1)

$5x + 15y = 1850$ --- (2)

Divide (2) through by 5

$x + 3y = 370$ --- (3)

Subtract (1) from (3)

$x - x + 3y - y = 370 - 160$

$2y = 210$

Divide through by 2

$y = \frac{210}{2}$

$y = 105$

Substitute 105 for y in (1)

$x + y = 160$

Make x the subject

$x = 160 - y$

Substitute 105 for y

$x = 160 - 105$

$x = 55$

Hence:

Mechanic 1: $55 per hour

Mechanic 2: $105 per hour

7 0

2 years ago