Question

What is the measure of angle p?

Answer 1

See explanation.

Explanation:

We have all sides of the triangle, so we can calculate the trigonometric function value of angle `P`:

`sinP=12/13~~0.9231`

The angle is

`P~~67.38^o`

Answer 2

67.38

Explanation:

Since `triangle PQR` is a right-angled triangle, we can use the cosine or sine or tan rule to find the `angle P`

(1) Sine

`sin angleP = "opposite"/"hypotenuse" = 12/13`

`angle P = sin^(-1)(12/13) = 67.38`

(2) Cosine

`cos angle P = "adjacent"/"hypotenuse" = 5/13`

`angle P = cos^(-1)(5/13) = 67.38`

(3) tan

`tan angleP = "opposite"/"adjacent" = 12/5`

`angleP = tan^(-1)( 12/5) = 67.38`

Hence, you can see that whichever rule you use, you will always get the same answer!