In triangle PQR, q= 8cm ,r=6cm and cos p=1/12. calculate the value of p
Careful about your notation.
Conventional notation is to refer to sides of a figure using small letters
and capital letters when referring to the vertices or angles of a triangle
So you meant to say: cos P = 1/12
anyway ....
you have the cosine law here,
p^2 = q^2 + r^2 - 2qr cosP
= 64 + 36 - 2(8)(6)(1/12)
= 92
So p = √92 = appr 9.59
To calculate the value of angle P, we can use the inverse cosine function (also known as arccosine).
Given that cos P = 1/12, we can find the value of P by taking the inverse cosine of 1/12.
P = arccos(1/12)
Using a calculator or trigonometric table, we can find that arccos(1/12) is approximately 84.26 degrees. Therefore, the value of angle P is approximately 84.26 degrees.
To calculate the value of angle P in triangle PQR, given side lengths q = 8 cm, r = 6 cm, and cos P = 1/12, we can use the inverse cosine function (arccosine).
First, we need to use the Law of Cosines to find side p, which is the side opposite angle P:
p^2 = q^2 + r^2 - 2qr * cos P
Substituting the given values:
p^2 = 8^2 + 6^2 - 2 * 8 * 6 * (1/12)
= 64 + 36 - 8 = 92
Taking the square root of both sides, we get:
p = √92
≈ 9.59 cm (rounded to two decimal places)
Now that we have the lengths of all three sides of the triangle, we can use the Law of Cosines again to find the value of angle P:
cos P = (q^2 + r^2 - p^2) / (2q * r)
Substituting the given values:
cos P = (8^2 + 6^2 - 9.59^2) / (2 * 8 * 6)
= (64 + 36 - 92) / 96
Simplifying the expression:
cos P = 8/96
= 1/12
Thus, we can conclude that the value of angle P is such that its cosine is 1/12.