In triangle PQR p=1.8cm q=2.5cm and r=3.6cm calculate P
Q
PQ = sqrt( (1.8)^2 + (2.5 - 1.8)^2 )
PQ = sqrt( 3.24 + 0.49 )
PQ = sqrt( 3.73 )
PQ = 1.93 cm
Did you mean:
calculate angle P ?
I will assume that's what you want:
by the cosine law:
1.8^2 = 2.5^2 + 3.6^2 - 2(2.5)(3.6)cos P
18cosP = 6.25+12.96-3.24
cosP = 15.97/18
angle P = 41.58°
I have no idea what our resident bot is trying to do.
Looks like it is trying to work something with Pythagoras, assuming
there is a right angle. Of course that is nosense.
To calculate the length of side P in triangle PQR, we can use the law of cosines. The law of cosines states that in any 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 lengths of those two sides, multiplied by the cosine of the included angle.
In our case, we are given all three sides of triangle PQR, so we can use the following formula:
P^2 = Q^2 + R^2 - 2 * Q * R * cos(PQR)
Let's plug in the values:
P^2 = (2.5cm)^2 + (3.6cm)^2 - 2 * (2.5cm) * (3.6cm) * cos(PQR)
Now we need to find the cosine of angle PQR. To do this, we can use the law of cosines again:
cos(PQR) = (Q^2 + R^2 - P^2) / (2 * Q * R)
Let's calculate cos(PQR) first:
cos(PQR) = (2.5cm^2 + 3.6cm^2 - P^2) / (2 * 2.5cm * 3.6cm)
Now we substitute this value of cos(PQR) back into the earlier equation and solve for P:
P^2 = (2.5cm)^2 + (3.6cm)^2 - 2 * (2.5cm) * (3.6cm) * [(2.5cm^2 + 3.6cm^2 - P^2) / (2 * 2.5cm * 3.6cm)]
Simplifying the equation:
P^2 = 6.25cm^2 + 12.96cm^2 - 4.5cm^2 - P^2
Move P^2 terms to one side:
2P^2 = 6.25cm^2 + 12.96cm^2 - 4.5cm^2
2P^2 = 14.71cm^2
Divide by 2:
P^2 = 14.71cm^2 / 2
P^2 = 7.355cm^2
Taking the square root:
P = √(7.355cm^2)
Calculating the value:
P ≈ 2.71cm
Therefore, the length of side P in triangle PQR is approximately 2.71cm.
To calculate the length of side P in triangle PQR, 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 lengths of those sides multiplied by the cosine of the angle between them.
In this case, we need to find side P, so we'll use the formula:
P^2 = Q^2 + R^2 - 2QRCos(P)
To calculate P, we need to know the measure of angle P. Without that information, we cannot find the exact value of side P.
If you have the measure of angle P, you can substitute the values of Q, R, and the angle into the formula and solve for P.