Question

The diagram shows three points P, Q and R on horizontal ground.
PQ = 50 m, PR = 100 m and angie PQR = 140°.
Calculate angle PRO.

Answer 1

Answer:

m<PQR = 18.7°

Step-by-step explanation:

Apply the Law of Sines,

$\frac{Sin A}{a} = \frac{Sin B}{b}$

Where,

Sin A = Sin 140

a = 100 m

Sin B = Sin R (<PRQ)

b = 50 m

Substitute

$\frac{Sin 140}{100} = \frac{Sin R}{50}$

Cross multiply

$100*Sin(R) = 50*Sin(140)$

Divide both sides by 100

$Sin(R) = \frac{50*Sin(140)}{100}$

$Sin(R) = 0.32139$

$R = Sin^{-1}(0.32139)$

R ≈ 18.7° (nearest tenth)

m<PQR = 18.7°

Answer 2

The angle PRO is 1.7 degrees.

Given that,

The diagram shows three points P, Q, and R on horizontal ground.

PQ = 50 m, PR = 100 m and angle PQR = 140°.

We have to determine,

The angle PRO.

According to the question,

The value of angle PRO is determined by using the sin rule-following all the steps given below.

$\rm \dfrac{sina}{a} = \dfrac{sinb}{b}$

Where,  Sin A = Sin 140 , a = 100 m , Sin B = Sin R (<PRQ) , b = 50 m

Substitute all the values in the formula,

$\rm \dfrac{sin140}{100} = \dfrac{sinR}{50}\\\\ \dfrac{0.64}{100} = \dfrac{sinR}{50}\\\\0.0064 = \dfrac{sinR}{50}\\\\0.0064 \times 50 = sinR\\\\0.321 = sinR\\\\R = sin{-1}(0.321)\\\\R = 18.7 \ degree$

Hence, The angle PRO is 1.7 degrees.

For more details refer to the link given below.

https://brainly.com/question/12895249