A man walks 55kmin the direction 0.36 degree from a point P to a point Q.He then walk 31km in the direction 137 degree from a point Q to a point T.How far is then from point P to point Q
Yes
To find the distance from point P to point Q, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the included angle.
Let's break down the given information:
- The man walks 55 km in the direction of 0.36 degrees from point P to point Q.
- The man walks 31 km in the direction of 137 degrees from point Q to point T.
Now, we need to find the distance from point P to point Q. Let's label it as PQ.
Using the law of cosines, we have:
PQ^2 = 55^2 + 31^2 - 2(55)(31)cos(theta)
To find the value of theta (the included angle), we can use the following formula:
theta = 180 - (alpha + beta), where alpha and beta are the given angles.
In this case, we have:
alpha = 0.36 degrees
beta = 137 degrees
Substituting these values into the formula, we can find the value of theta.
Then, we can substitute the value of theta into the law of cosines equation and solve for PQ.
Remember to convert the angle measurements to radians when using the cosine function.
Once we have the value of PQ from the equation, we take the square root to find the distance from point P to point Q.
55km, as you stated.
But, to find the distance from T to P, use the law of cosines