Villages p, q and r are situated as follows, p is 15km due north of q and the bearings of p and q are 50 degree and 80 degree respectively. Calculate the distance of r from p and q
I appears that you have a triangle PQR , with PQ = 15 km,
and angle P = 50°, angle Q = 80°
A quick mental calculation gives us angle R = 50° , making the triangle isosceles.
So without any work, QR = 15 km
by the sine law:
PR/sin80 = 15/sin50
PR = 15sin80/sin50
= ...
let me know if I misunderstood your description.
Village P Q and R are situated as follows .P is 15km due north of Q and the bearing of P and Q from R are 50° and 80° respectively . calculate to the nearest 0.5 km the distance of R from P and Q
IN ABC C=53°,b=3.56,c=4.28
To calculate the distance of village r from villages p and q, we need to use trigonometric concepts and the given information about the bearings.
Let's start by visualizing the given information:
1. Village p is located 15km due north of village q.
2. The bearing of village p is 50 degrees.
3. The bearing of village q is 80 degrees.
First, let's calculate the distance between village p and r:
To find the distance of r from p, we can use trigonometry and consider that r is in a right-angled triangle formed by p and q.
Since we know the bearing of p is 50 degrees, we can conclude that the angle below village p is 40 degrees (90 - 50). This angle, let's call it angle A.
Using basic trigonometry, we can say that:
tan(A) = opposite/adjacent
The opposite side is the distance we need to find, which is the distance between p and r. Let's call it x.
So, tan(40) = x/15
Solving for x:
x = tan(40) * 15
Using a calculator or software to find the tangent of 40 degrees and then multiplying by 15, we get:
x ≈ 15.5 km (rounded to one decimal place)
Therefore, the distance between p and r is approximately 15.5 km.
Next, let's calculate the distance between village q and r:
To find the distance of r from q, we can use the same triangle formed by p, q, and r. Now we consider that angle B is the angle below village q and the angle we need to focus on.
Since we know the bearing of q is 80 degrees, we can conclude that angle B is 10 degrees (90 - 80).
Using the same trigonometry concept as before:
tan(B) = x'/15
Solving for x':
x' = tan(10) * 15
Using a calculator or software to find the tangent of 10 degrees and then multiplying by 15, we get:
x' ≈ 2.6 km (rounded to one decimal place)
Therefore, the distance between q and r is approximately 2.6 km.
In summary, the distance between village p and r is approximately 15.5 km, and the distance between village q and r is approximately 2.6 km.