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13.11.2020

In PQR, the measure of

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Mathematics

I) Construct a triangle PQR such that |PQ|=8cm,{RPQ=90°{PQR=30°.Measure |RQ|

Step-by-step answer

P Answered by Master

6.93 cm

Step-by-step explanation:

You have a right triangle (90°), so you do as follow:

If I understand correctly, you are looking for the hypotenuse so

$cos(30) = \frac{PQ}{QR} = \frac{8 cm}{QR}$

That is equal to QR = cos(30)*8 cm = 6.928 cm

Mathematics

I) Construct a triangle PQR such that |PQ|=8cm,{RPQ=90°{PQR=30°.Measure |RQ|

Step-by-step answer

P Answered by Master

6.93 cm

Step-by-step explanation:

You have a right triangle (90°), so you do as follow:

If I understand correctly, you are looking for the hypotenuse so

$cos(30) = \frac{PQ}{QR} = \frac{8 cm}{QR}$

That is equal to QR = cos(30)*8 cm = 6.928 cm

Mathematics

List the sides of each triangle in order from shortest to longest {pictures are attached below} 1. in δpqr, the measure of angle p = 55, the measure of angle q = 82 and the measure of angle r = 43. list the sides of the triangle in order from shortest to longest (no picture was provided). 2. in δmns, mn = 7, ns = 5, and ms = 9. list the angles of the triangle in order from smallest to largest (no picture was provided). 3. two sides of a triangle have side lengths 8 units and 17 units. describe the lengths (x) that are possible for the third side

Step-by-step answer

P Answered by Master

For 1:

PQ < QR < PR

For 2:

NS < MN < MS

For 3:

17-8 < x < 17+8

Step-by-step explanation:

For 1:

The side opposite to the smallest angle will be the shortest.

So, from the image ∠R is the smallest, fso the side opposite to it, which is PQ will be the shortest.

The largest side will be the side whcih is opposite to ∠Q which is PR.

So the order of sides from smallest to largest is:

PQ < QR < PR

For 2:

Length of MN = 7 units

Length of MS = 9 units

Length of NS = 5 units

The order of the sides from smallest to largest is:

NS < MN < MS

For 3:

We are given two sides of the triangle which sre 17 units and 8 units and third side is taken 'x'.

So the third side 'x' will lie between the difference of the two sides and the sum of the two sides.

So, the length of 'x' will be:

17-8 < x < 17+8

List the sides of each triangle in order from shortest to longest {pictures are attached below} 1. i

Mathematics

Step-by-step answer

P Answered by Master

For 1:

PQ < QR < PR

For 2:

NS < MN < MS

For 3:

17-8 < x < 17+8

Step-by-step explanation:

For 1:

The side opposite to the smallest angle will be the shortest.

So, from the image ∠R is the smallest, fso the side opposite to it, which is PQ will be the shortest.

The largest side will be the side whcih is opposite to ∠Q which is PR.

So the order of sides from smallest to largest is:

PQ < QR < PR

For 2:

Length of MN = 7 units

Length of MS = 9 units

Length of NS = 5 units

The order of the sides from smallest to largest is:

NS < MN < MS

For 3:

We are given two sides of the triangle which sre 17 units and 8 units and third side is taken 'x'.

So the third side 'x' will lie between the difference of the two sides and the sum of the two sides.

So, the length of 'x' will be:

17-8 < x < 17+8

Mathematics

In ΔPQR, the measure of ∠R=90°, the measure of ∠P=52°, and QR = 9.6 feet. Find the length of RP to the nearest tenth of a foot.

Step-by-step answer

P Answered by PhD

Given:

In ΔPQR, the measure of ∠R=90°, the measure of ∠P=52°, and QR = 9.6 feet.

We need to determine the length of RP.

Length of RP:

The image of the triangle PQR is attached below.

Using the figure, the length of RP can be determined using the trigonometric ratio,

$tan \ \theta=\frac{opp}{adj}$

Substituting $\theta=52^{\circ}$ , opp=QR and adj=RP

Thus, we get;

$tan \ 52^{\circ}=\frac{QR}{RP}$

Substituting the values, we get;

$1.2799=\frac{9.6}{RP}$

Simplifying, we get;

$RP=\frac{9.6}{1.2799}$

Dividing, we get;

RP=7.5

Thus, the length of RP is 7.5 feet.

In ΔPQR, the measure of ∠R=90°, the measure of ∠P=52°, and QR = 9.6 feet. Find the length of RP to t

Mathematics

In triangle pqr, the measure of zr=90°, the measure of zp=51°, and qr = 38 feet. find the length of pq to the nearest tenth of a foot.

Step-by-step answer

P Answered by PhD

Therefore Length of PQ is 48.9 foot.

Step-by-step explanation:

Given:

In Triangle PQR,

∠R = 90°

∠P = 51°

QR = 38 feet = side opposite to angle P

To Find:

PQ = ? = Hypotenuse

Solution:

In Right angle Triangle PQR Cosine Identity we get,

$\sin P = \dfrac{\textrm{side opposite to angle P}}{Hypotenuse}\\$

Substituting the values we get,

$\sin 51 = \dfrac{QR}{PQ}=\dfrac{38}{PQ}\\\\0.7771=\dfrac{38}{PQ}\\\\PQ=\dfrac{38}{0.7771}=48.899\\\\\therefore PQ=48.9\ foot$

Therefore Length of PQ is 48.9 foot.

Mathematics

In ΔPQR, the measure of ∠R=90°, the measure of ∠P=26°, and PQ = 8.5 feet. Find the length of QR to the nearest tenth of a foot.

Step-by-step answer

P Answered by Specialist

3.7feet

Step-by-step explanations

Using the sin rule

A/sin a = B/sin b

Let A = PQ = 8.5feet

B = QR = x feet

a = R = 90°

b = P = 26°

Substitute the values into the Sin rule

8.5/sin90 = x/sin26

8.5×sin 26 = x × sin 90

8.5×0.4383 = x× 1

3.7255 = x

Hence the length of QR to the nearest tenth 3.7feet

In ΔPQR, the measure of ∠R=90°, the measure of ∠P=26°, and PQ = 8.5 feet. Find the length of QR to t

Mathematics

In PQR the measure of R=90 the measure of P=62 and RP=8.6 find the length of QR to the nearest tenth of a foot.

Step-by-step answer

P Answered by Specialist

QR = 4.6 ft

Step-by-step explanation:

By applying tangent rule in the given triangle PQR,

tan(62°) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

= $\frac{8.6}{QR}$

QR = $\frac{8.6}{\text{tan}(62)}$

QR = 4.573

QR ≈ 4.6 ft

In PQR the measure of R=90 the measure of P=62 and RP=8.6 find the length of QR to the nearest tenth

Mathematics

In ΔPQR, the measure of ∠R=90°, the measure of ∠P=26°, and PQ = 8.5 feet. Find the length of QR to the nearest tenth of a foot.

Step-by-step answer

P Answered by Specialist

3.7feet

Step-by-step explanations

Using the sin rule

A/sin a = B/sin b

Let A = PQ = 8.5feet

B = QR = x feet

a = R = 90°

b = P = 26°

Substitute the values into the Sin rule

8.5/sin90 = x/sin26

8.5×sin 26 = x × sin 90

8.5×0.4383 = x× 1

3.7255 = x

Hence the length of QR to the nearest tenth 3.7feet

Mathematics

In pqr the measure of r is 90 degrees the measure of q is 38 degrees and qr is 8.8 feet. Find the length of pq to the nearest tenth of a foot

Step-by-step answer

P Answered by Master

11.2 feets

Step-by-step explanation:

Angle, P = 180 - (38 + 90) = 52

Using trigonometry :

Length pq:

SinP = opposite / hypotenus

Sin52 = 8.8 / pq

0.7880107 * pq = 8.8

pq = 8.8 / 0.7880107

pq = 11.167361

Hence, length of pq = 11.2 feets

In pqr the measure of r is 90 degrees the measure of q is 38 degrees and qr is 8.8 feet. Find the le

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