The angle p, to the nearest degree, in a triangle with side lengths p=15cm, q=19cm and r=22cm, is?
I missed a class to get corona tested and my teacher says its my fault that I don't know how to do this. My friend tried to explain it to me but Im not sure he understands it either. Help!
If p,q,r are sides, then p is not an angle. Maybe you meant P.
So use the law of cosines.
p^2 = q^2 + r^2 - 2qr cosP
15^2 = 19^2 + 22^2 - 2*19*22 cosP
cosP = 155/209
P = 42.13°
To find the angle p in a triangle with side lengths 15cm, 19cm, and 22cm, you can use the Law of Cosines. The formula for the Law of Cosines is:
c^2 = a^2 + b^2 - 2ab * cos(C)
Where c is the length of the side opposite to the angle C, and a and b are the lengths of the other two sides.
In this case, let's label p as the angle opposite to the side with length 15cm, q as the angle opposite to the side with length 19cm, and r as the angle opposite to the side with length 22cm.
Using the Law of Cosines, we can rearrange the formula as:
cos(p) = (a^2 + b^2 - c^2) / (2ab)
Substituting the given values, we have:
cos(p) = (15^2 + 19^2 - 22^2) / (2 * 15 * 19)
Now calculate:
cos(p) = (225 + 361 - 484) / 570
cos(p) = 102 / 570
cos(p) ≈ 0.1789
To find the angle p, we need to find the inverse cosine (cos^-1) or arccosine of 0.1789. Using a calculator, you can determine:
p ≈ 79.45 degrees
Therefore, to the nearest degree, the angle p in the triangle with side lengths 15cm, 19cm, and 22cm is approximately 79 degrees.
Don't worry, I'm here to help you understand how to solve this problem step by step.
To find the angle, we can use the Law of Cosines, which 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 included angle.
The formula for the Law of Cosines is:
c^2 = a^2 + b^2 - 2ab * cos(C),
where c is the side opposite angle C, and a and b are the other two sides.
In this case, you have side lengths p=15cm, q=19cm, and r=22cm. Let's assume that the angle we want to find is angle p.
Using the Law of Cosines, we can write the equation as:
p^2 = q^2 + r^2 - 2qr * cos(p).
Plugging in the values we have:
15^2 = 19^2 + 22^2 - 2 * 19 * 22 * cos(p).
Now, we can rearrange the equation to solve for cos(p):
cos(p) = (19^2 + 22^2 - 15^2) / (2 * 19 * 22).
cos(p) = (361 + 484 - 225) / (2 * 19 * 22).
cos(p) = 620 / 836.
cos(p) ≈ 0.741.
To find the angle p, we need to take the inverse cosine (also known as arccos) of the value we just calculated:
p ≈ arccos(0.741) ≈ 42.6 degrees.
Therefore, the angle p, to the nearest degree, is approximately 43 degrees.