Mathematics, 27.07.2021 22:00 dios01

Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and ∠PAL = 93°. Find the area of the circle enclosed by line PL and arc PL. Show all work and round your answer to two decimal places.

Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and ∠PAL = 93°. Fin

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Answer from: yoboi33

The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.

The calculation of the area between line segment PL and circle arc PL is described below:

1) Calculation of the area of the circle arc.

2) Calculation of the area of the triangle.

3) Subtracting the area found in 2) from the area found in 1).

Step 1:

The area of a circle arc is determined by the following formula:

$A_{ca} = \frac{\alpha\cdot \pi\cdot r^{2}}{360}$ (1)

Where:

$A_{ca}$ - Area of the circle arc.

$\alpha$ - Arc angle, in sexagesimal degrees.

- Radius.

If we know that $\alpha = 93^{\circ}$ and r = 11 , then the area of the circle arc is:

$A_{ca} = \frac{93\cdot \pi\cdot 11^{2}}{360}$

$A_{ca} \approx 98.201$

Step 2:

The area of the triangle is determined by Heron's formula:

$A_{t} = \sqrt{s\cdot (s-l)\cdot (s-r)^{2}}$ (2)

$s = \frac{l + 2\cdot r}{2}$

Where:

$A_{t}$ - Area of the triangle.

- Radius.

- Length of the line segment PL.

If we know that l = 16 and r = 11 , then the area of the triangle is:

$s = \frac{16+2\cdot (11)}{2}$

s = 19

$A_{t} = \sqrt{19\cdot (19-16)\cdot (19-11)^{2}}$

$A_{t} \approx 60.399$

Step 3:

And the area between the line segment PL and the circle arc PL is:

$A_{s} = A_{ca}-A_{t}$

$A_{s} = 98.201 - 60.399$

$A_{s} = 37.802$

The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.

Answer from: Quest

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

Answer from: Quest

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that runner b is moving at a slower rate."

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